Sharp bounds of population causal parameters under Assumptions 1--3

1. Sharp bounds of $\bar{\delta}(1)$ (NIE(1))

Lower bound

\max\left\{\begin{matrix}
p001.0 - p001.1 - p010.1 + p101.1 - p110.1 + p111.0 - 1\\- p000.0 + p000.1 - p011.0 + p101.1 + p111.1 - 1\\- p000.0 - p001.1 - p010.1 - p011.0 - p100.0 - p110.1\\- p000.0 + p000.1 - p011.0 - p011.1 + p100.0 - p100.1 - 1\\- p001.0 + p101.1 - p110.0 + p110.1 - 1\\- p001.0 + p001.1 - p010.0 + p101.1 - p110.0 + p110.1 - 1\\- p000.0 - p011.0 + p011.1 - p100.0 + p101.1 + p111.0 - 1\\- p001.0 + p001.1 - p010.0 + p101.1 - p110.0 + p111.0 - 1\\p101.1 + p111.0 - 1\\- p000.0 - p001.0 - p001.1 - p010.1 - p011.0 - p011.1 - p100.1 - p110.0\\- p000.0 - p011.0 + p011.1 - p100.0 + p101.0 + p111.0 - 1\\- p000.0 - p001.0 - p001.1 - p010.0 - p011.0 - p011.1 - p100.1 - p110.1\\- p011.1 + p100.0 - p100.1 + p101.0 + p111.0 - 1\\- p001.0 + p001.1 - p010.0 + p101.0 - p110.0 + p111.0 - 1\\p101.0 + p111.0 - 1\\- p001.1 + p101.0 + p110.0 - p110.1 + p111.0 - 1\\- p001.1 + p010.0 - p010.1 + p101.0 + p111.0 - 1\\- p000.0 - p001.0 - p011.0 + p011.1 - p100.0 + p101.1 - p110.0 + p110.1 - 1\\- p001.0 + p001.1 - p010.0 + p101.0 - p110.0 + p111.1 - 1\\p101.0 + p111.1 - 1\\- p000.0 - p011.0 + p011.1 - p100.0 + p101.0 + p111.1 - 1\\- p001.0 - p010.0 + p010.1 - p011.0 + p101.1 + p111.0 - 1\\p000.0 + p001.1 + p010.1 + p100.0 + p101.0 + p101.1 + 2 p111.0 - 2\\p010.1 - p011.0 + p011.1 + p101.0 + p101.1 + p110.0 + 2 p111.0 - 2\\- p000.1 - p001.0 - p010.0 - p011.1 - p100.1 - p110.0\\p000.0 - p000.1 - p011.1 + p101.0 + p111.0 - 1\\p000.0 - p000.1 - p011.0 - p011.1 - p100.0 + p100.1 - 1\\- p001.0 - p010.0 + p010.1 + p101.1 + p111.1 - 1\\- p000.1 + p011.0 - p011.1 - p100.1 + p101.1 + p111.0 - 1\\- p000.1 - p001.0 - p010.0 + p010.1 - p011.1 - p100.1 + p101.1 + p111.0 - 1\\- p000.1 - p001.0 + p011.0 - p011.1 - p100.1 + p101.1 - p110.0 + p110.1 - 1\\- p000.1 - p001.0 - p001.1 - p010.0 - p011.0 - p011.1 - p100.0 - p110.1\\- p001.0 - p001.1 - p010.0 + p010.1 + p110.0 - p110.1 - 1\\- p000.1 + p011.0 - p011.1 - p100.1 + p101.0 + p111.1 - 1\\- p000.1 + p011.0 - p011.1 - p100.1 + p101.1 + p111.1 - 1\\- 2 p000.1 - p001.0 - p001.1 - p010.0 - 2 p011.1 - 2 p100.1 - p110.1\\- 2 p000.1 - p001.0 - p001.1 - p010.1 + p011.0 - 2 p011.1 - 2 p100.1 - p110.0 - p111.0\\- p001.0 - p001.1 + p010.0 - p010.1 - p110.0 + p110.1 - 1\\- p011.0 - p100.0 + p100.1 + p101.1 + p111.1 - 1\\- p000.1 - p001.0 - p001.1 - p010.1 - p011.0 - p011.1 - p100.0 - p110.0\\p101.1 + p111.1 - 1\\- p001.0 + p101.1 - p110.0 + p110.1 + p111.1 - 1\\p001.0 - p001.1 - p010.1 + p101.0 - p110.1 + p111.1 - 1\\p001.0 - p001.1 - p010.1 + p101.1 - p110.1 + p111.1 - 1
\end{matrix}\right\}

Upper bound

\min\left\{\begin{matrix}
p000.0 + p010.1 + p100.0 + p101.1 + p110.1 + p111.0\\p000.1 - 2 p001.0 + p001.1 - p010.0 + p010.1 - 2 p011.0 + p011.1 + p100.1 - p101.0 + p101.1 - p110.0 + p110.1 + 1\\p000.0 + p000.1 + p010.1 - p011.0 + p011.1 + p100.0 + p100.1 + p101.1 + p110.1 + p111.0\\p000.0 + p000.1 - p001.0 + p001.1 + p010.1 + p100.0 + p100.1 + p101.1 + p110.1 + p111.0\\- p001.0 - p011.0 + p101.1 - p110.0 + p110.1 + 1\\3 p000.1 - p001.0 + 2 p001.1 + 2 p010.1 - p011.0 + 3 p011.1 + 3 p100.1 + 3 p101.1 - p110.0 + 3 p110.1 + 2 p111.1 - 1\\p010.0 - p010.1 + p101.0 + p101.1 - p110.0 + p110.1 + 1\\- p001.0 - p010.0 + p010.1 - p011.0 + p101.1 + 1\\- p010.0 + p010.1 + p101.0 + p101.1 + p110.0 - p110.1 + 1\\p000.1 - p001.0 - p010.0 + p010.1 - 2 p011.0 + p011.1 + p100.1 + p101.1 + p111.0 + 1\\p000.1 + p010.0 + p100.1 + p101.0 + p110.0 + p111.1\\- p001.1 - p011.1 + p101.0 + p110.0 - p110.1 + 1\\p000.1 - p001.1 - p011.0 + p100.1 - p111.0 + p111.1 + 1\\p000.1 - p001.1 - p011.0 + p100.1 + p101.0 + p110.0 - p110.1 + p111.1 + 1\\p000.1 - p001.1 + p010.0 - p010.1 + p100.1 + p101.0 - p111.0 + p111.1 + 1\\- p001.0 - p011.0 - p100.0 + p100.1 + p111.1 + 1\\- p000.0 + p000.1 - p001.0 - p011.0 + p111.1 + 1\\- p001.0 - p011.0 + 1\\- p001.0 + p010.0 - p011.0 + p101.0 - p101.1 + p110.0 + 1\\- p000.0 + p000.1 - p001.0 - p010.0 + p010.1 - p011.0 + p101.1 + p111.1 + 1\\- p001.0 - p010.0 + p010.1 - p011.0 - p100.0 + p100.1 + p101.1 + p111.1 + 1\\p000.1 + p010.0 + p011.1 + p100.1 + p101.0 + p101.1 + p110.1 + p111.1\\- p001.1 - p011.0 + 1\\- p000.0 - p001.0 - p001.1 - 2 p011.0 - p100.0 - p101.1 - p110.1 + 2\\- p001.1 - p011.0 + p101.0 + p110.0 - p110.1 + p111.0 + 1\\p000.1 + p010.0 + p011.1 + p100.1 + p101.0 + p110.0 + p110.1 + p111.1\\- p001.1 + p010.0 - p011.0 + p101.0 - p101.1 + p110.0 + 1\\p000.1 - p001.0 - p011.1 + p100.1 - p111.0 + p111.1 + 1\\p000.1 - p001.1 - p011.1 + p100.1 - p111.0 + p111.1 + 1\\p000.1 - p001.1 - p011.1 + p100.1 + p101.0 + p110.0 - p110.1 + p111.1 + 1\\2 p000.1 + p010.0 + p011.0 + 2 p100.1 + p101.0 + p101.1 + p110.1 - p111.0 + 2 p111.1\\- p001.0 - p011.1 + 1\\- p001.0 + p010.0 - p011.1 + p101.0 - p101.1 + p110.0 + 1\\p000.0 + p001.1 + p010.1 + p011.1 - p100.0 + 2 p100.1 + p101.1 + p110.1 + p111.0 + 2 p111.1\\- p000.0 + 2 p000.1 + p001.1 + p010.1 + p011.1 + p100.0 + p101.1 + p110.1 + p111.0 + 2 p111.1\\- p000.0 + p000.1 - p001.0 - p011.0 + p101.1 - p110.0 + p110.1 + p111.1 + 1\\- p001.1 + p010.1 - p011.0 - p101.0 + p101.1 + p110.1 + 1\\p000.1 + p010.1 + p100.0 + p101.1 + p110.1 + p111.0 + p111.1\\- p001.1 + p010.1 - p011.1 - p101.0 + p101.1 + p110.1 + 1\\- p001.0 + p010.1 - p011.1 - p101.0 + p101.1 + p110.1 + 1\\p000.0 + p010.1 + p100.1 + p101.1 + p110.1 + p111.0 + p111.1\\- p001.1 + p010.0 - p010.1 - p011.1 + p101.0 + 1\\- p001.1 - p011.1 + 1\\- p001.0 - p011.0 - p100.0 + p100.1 + p101.1 - p110.0 + p110.1 + p111.1 + 1
\end{matrix}\right\}

2. Sharp bounds of $\bar{\delta}(0)$ (NIE(0))

Lower bound

\max\left\{\begin{matrix}
p000.1 + p010.1 - p101.0 + p101.1 - p110.0 + p111.0 - 1\\p000.1 - p001.0 + p001.1 + p010.1 - p110.0 + p111.0 - 1\\- p001.0 - p011.1 - p100.1 - p101.0 - p110.0 - p110.1 + p111.0 - p111.1\\p000.1 + p010.0 + p111.0 - 1\\p000.1 + p010.1 - p011.1 + p100.0 - p100.1 + p111.0 - p111.1 - 1\\p000.1 + p010.1 + p111.0 - 1\\p000.1 - p001.1 + p010.1 - p101.1 + p110.0 - p110.1 + p111.0 - 1\\p000.1 + p010.0 - p011.1 + p100.0 - p100.1 + p111.0 - p111.1 - 1\\p000.1 - p001.1 + p010.0 - p101.1 + p110.0 - p110.1 + p111.0 - 1\\p000.0 + p010.1 - p011.1 + p100.0 - p100.1 - p110.1 + 2 p111.0 - p111.1 - 1\\p000.1 + p010.1 - p011.0 + p011.1 - p100.0 + p111.0 - 1\\p000.0 + p001.0 - p001.1 + p010.0 - p100.1 - p110.1 + 2 p111.0 - p111.1 - 1\\p000.0 + p010.0 - p100.1 + p101.0 - p101.1 - p110.1 + 2 p111.0 - p111.1 - 1\\p000.0 + p010.0 - p100.1 - p110.1 + 2 p111.0 - p111.1 - 1\\p000.0 + p010.1 - p011.0 - p100.1 - p110.1 + 2 p111.0 - p111.1 - 1\\- p001.1 - p011.1 - p100.0 - p100.1 - p101.1 - p110.1\\- p001.1 - p011.1 - p100.0 - p100.1 - p101.0 - p110.0 - p110.1\\- p001.0 - p011.1 - p100.0 - p100.1 - p101.1 - p110.0 - p110.1\\p000.0 + p010.0 + p011.0 - p011.1 - p100.1 - p110.1 + p111.0 - 1\\p000.0 - p000.1 - p001.1 - 2 p011.1 - 2 p100.1 - p101.1 - 2 p110.1 + p111.0 - p111.1\\- p001.0 - p011.1 - p100.1 - p101.0 - p110.0 - p111.1\\p000.0 + p010.0 - p100.1 + p111.0 - p111.1 - 1\\- p001.1 - p011.0 - p100.0 - p101.1 - p110.1\\p000.0 + p001.0 - p001.1 + p010.0 - p110.1 + p111.0 - 1\\p000.0 + p010.0 + p011.0 - p011.1 - p100.1 - 1\\p000.0 + p010.0 + p101.0 - p101.1 - p110.1 + p111.0 - 1\\- p001.1 + p010.0 - p010.1 - p011.0 - p011.1 - p100.0 - p101.1 - p110.1 - p111.1\\p000.0 + p010.0 + p111.0 - 1\\p000.0 - p000.1 - p001.1 + p010.0 - p010.1 - p011.0 - p011.1 - p100.0 - p101.1 - p110.1 - p111.1\\p000.0 + p010.1 - p011.1 + p100.0 - p100.1 + p111.0 - p111.1 - 1\\p000.0 + p010.1 + p111.0 - 1\\p000.0 - p000.1 - p001.1 - p011.0 - p011.1 - p100.0 - p101.1 - p110.1 - p111.1\\p000.0 - p001.1 + p010.1 - p101.1 + p110.0 - p110.1 + p111.0 - 1\\p001.0 - p001.1 - p101.0 + p101.1 - p110.0 - p110.1 + p111.0 - 1\\- p001.0 + p001.1 + p101.0 - p101.1 - p110.0 - p110.1 + p111.0 - 1
\end{matrix}\right\}

Upper bound

\min\left\{\begin{matrix}
p000.0 + p000.1 + p001.0 + p010.0 + p010.1 + p101.0 + p111.1\\p000.0 + p010.0 - p011.1 - p100.1 + p101.0 - p101.1 - p110.1 + 1\\p000.0 + p001.0 - p001.1 + p010.0 - p011.1 - p100.1 - p110.1 + 1\\p000.0 - p011.1 - p100.1 - p110.1 + 1\\p000.0 + p000.1 + p001.0 + p010.0 + p010.1 + p101.0 + p110.0 - p110.1 + p111.0 + p111.1\\p000.1 - p100.0 - p110.0 - p111.0 + p111.1 + 1\\- p000.0 + p000.1 - p011.0 + p011.1 - p100.0 - p110.1 + p111.1 + 1\\p000.1 + p001.0 + p010.0 + p011.1 + p101.0 + p111.1\\- p001.0 + p001.1 + p010.0 + p010.1 - p011.0 + p101.0 - p101.1 + 1\\p001.0 - p001.1 + p010.0 + p010.1 - p011.0 - p101.0 + p101.1 + 1\\p000.0 - p000.1 - p100.0 - p110.1 + p111.0 + 1\\- p011.0 - p100.0 - p110.1 + 1\\p001.1 - p010.0 + p010.1 - p011.0 - p100.0 + p101.1 - p110.1 + 1\\p000.0 - p000.1 - p100.1 - p110.0 + p111.0 + 1\\p000.0 - p000.1 - p100.0 - p110.0 + p111.0 + 1\\p000.1 - p011.0 + p011.1 - p100.0 - p110.0 + 1\\- p011.0 - p100.0 - p110.0 + 1\\p000.0 + p001.1 + p010.0 + p010.1 + p101.0 + p111.0\\p000.0 + p001.0 + p010.0 + p010.1 + p101.1 + p111.0\\p000.0 + p001.1 + p010.1 + p101.1 + p111.0\\p000.1 + p010.1 - 2 p011.0 + p011.1 - p100.0 - p110.1 + p111.0 + 1\\p000.0 - p011.0 - p100.1 - p110.1 + p111.0 - p111.1 + 1\\p000.1 + p010.1 - 2 p011.0 + p011.1 - p100.0 - p110.0 + 1\\p000.1 - p001.0 + p001.1 + p010.1 - 2 p011.0 + p011.1 - p100.0 - p110.0 + 1\\p000.1 + p010.1 - 2 p011.0 + p011.1 - p100.0 - p101.0 + p101.1 - p110.0 + 1\\p001.1 - p010.0 + p010.1 - p011.0 - p100.1 + p101.1 - p110.0 + 1\\- p011.0 - p100.1 - p110.0 + 1\\p001.1 - p010.0 + p010.1 - p011.0 - p100.1 + p101.1 - p110.1 + 1\\p001.0 - p001.1 + p010.0 - p011.0 - p100.1 - p110.1 + 1\\p010.0 - p011.0 - p100.1 + p101.0 - p101.1 - p110.1 + 1\\- p011.0 - p100.1 - p110.1 + 1\\p001.0 - p001.1 + p010.0 - p011.0 - p100.1 + p101.0 - p101.1 - p110.1 + 1\\p001.0 - p001.1 + p010.0 - p011.0 - p100.1 + p101.0 - p101.1 + p110.0 - 2 p110.1 + p111.0 + 1\\- p000.0 + p000.1 - p011.0 + p011.1 - p100.1 - p110.1 + p111.1 + 1\\- p000.0 + p000.1 - p011.0 + p011.1 - p100.1 - p110.0 + p111.1 + 1
\end{matrix}\right\}

3. Sharp bounds of $\bar{\xi}(1)$ (NDE(1))

Lower bound

\max\left\{\begin{matrix}
- p000.0 + p000.1 - p001.1 + p010.0 - p010.1 + p101.0 + p111.1 - 1\\- p000.0 + p000.1 + p011.1 - p100.0 + p101.0 - p110.0 + p111.1 - 1\\- p000.0 + p000.1 + p101.0 + p111.1 - 1\\- p000.0 + p000.1 - p001.1 - p011.1 + p101.0 + p110.0 - p110.1 - 1\\- p000.0 + p000.1 - p001.1 - p011.1 + p100.0 - p100.1 + p101.0 - 1\\- p000.0 + 2 p000.1 + p010.0 + p100.1 + p101.0 + p101.1 + p110.0 + p111.1 - 2\\- p000.0 + 2 p000.1 + p010.1 + p100.0 + p101.0 + p101.1 + p110.0 + p111.1 - 2\\- p000.0 + 2 p000.1 + p010.0 + p100.0 + p101.0 + p101.1 + p110.1 + p111.1 - 2\\- p000.0 + p000.1 - 2 p001.0 + 2 p001.1 - 2 p010.0 + p011.1 - 2 p100.0 + p101.0 - 2 p110.0 + p111.1 - 1\\- p000.0 + p000.1 - p001.0 + p001.1 - p010.0 + p011.1 - p100.0 + p101.0 - p110.0 + p111.1 - 1\\- 2 p000.0 + 2 p000.1 - p001.0 - p011.0 + p101.1 - p111.0 + p111.1 - 1\\- p000.0 - 2 p001.0 + p001.1 - 2 p010.0 - 2 p100.0 - 2 p101.0 + 2 p101.1 - 2 p110.0\\- p000.0 - 2 p001.0 + p001.1 - 2 p010.0 - 2 p100.0 - 2 p101.0 + 2 p101.1 - 2 p110.0 + p110.1 - p111.0\\- p000.0 - 3 p001.0 + p001.1 - 2 p010.0 - 2 p100.0 - 2 p101.0 + 2 p101.1 - 3 p110.0 + 2 p110.1 - 2 p111.0\\- p000.0 - p001.0 - 2 p010.0 - 2 p100.0 - 2 p101.0 + 2 p101.1 - 2 p110.0\\- p000.0 - 2 p001.0 + p001.1 - 2 p010.0 - 2 p100.0 - 2 p110.0\\- p000.0 - p001.0 - p010.0 - p100.0 - p110.0\\- p000.0 - p001.0 - p001.1 - p010.0 - p011.1 - p100.0 - p110.1\\- p000.0 - p001.0 - p010.0 - p100.0 - p101.0 + p101.1 - p110.0\\- 2 p000.0 - p001.0 - p010.0 - p011.0 + p011.1 - 2 p100.0 - 2 p110.0\\- 2 p000.0 - p001.0 - p010.0 - p011.0 + p011.1 - 2 p100.0 - p101.0 + p101.1 - 2 p110.0\\- p000.0 - 2 p001.0 + p001.1 - 2 p010.0 - 2 p100.0 - p101.0 + p101.1 - 2 p110.0 + p110.1 - p111.0\\- p000.0 - 2 p001.0 - p010.0 - p100.0 - p101.0 + p101.1 - 2 p110.0 + p110.1 - p111.0\\- p000.0 - p001.0 - p001.1 - p010.0 - p011.1 - p100.1 - p110.0\\- p000.0 + p000.1 - p001.0 - p010.0 + p010.1 + p101.1 + p111.1 - 1\\- p000.0 + p000.1 - p001.0 - p001.1 + p010.0 - p010.1 - p100.0 + p100.1 + p111.1 - 1\\- p000.0 - p001.0 - 2 p001.1 + p010.0 - 2 p010.1 - p011.1 - p100.0 - p101.1 - p110.0\\- p000.0 - p001.0 - p001.1 - p010.1 - p100.0 - p110.0\\- p000.0 + p000.1 - p001.0 - p100.0 + p100.1 + p101.1 + p111.1 - 1\\- p000.0 + p000.1 - 2 p010.0 + p011.1 - 2 p100.0 - 2 p101.0 + 3 p101.1 - 2 p110.0 + p111.1 - 1\\- p000.0 + p000.1 - p001.0 - p001.1 + p010.0 - p010.1 - p110.0 + p110.1 + p111.1 - 1\\- p000.0 + p000.1 + p011.1 - p100.0 + p101.1 - p110.0 + p111.1 - 1\\- p000.0 + p000.1 + p101.1 + p111.1 - 1\\- p000.0 + p000.1 - p010.0 + p011.1 - p100.0 - p101.0 + 2 p101.1 - p110.0 + p111.1 - 1\\- p000.0 + p000.1 - p001.0 + p101.1 - p110.0 + p110.1 + p111.1 - 1\\- 3 p000.0 - 3 p001.0 - 2 p010.0 - 2 p011.0 + p011.1 - 3 p100.0 - 2 p101.0 + p101.1 - 3 p110.0 + p110.1 - 2 p111.0 + 1\\p000.1 + p001.0 + p010.0 + p011.0 + p011.1 + 2 p101.0 + 2 p111.1 - 2\\p000.1 - p001.0 + 2 p001.1 - p010.0 + p011.0 + p011.1 - p100.0 + 2 p101.0 - p110.0 + 2 p111.1 - 2\\p000.1 + p001.1 + p011.0 + p011.1 + 2 p101.0 + 2 p111.1 - 2\\- p000.1 - p001.0 - p010.0 - p011.1 - p100.0 - p101.0 + p101.1 - p110.0\\- p000.1 - 2 p001.0 - p010.0 - p011.1 - p100.0 - p101.0 + p101.1 - 2 p110.0 + p110.1 - p111.0\\p000.0 - p000.1 - p001.0 - p010.0 + p010.1 - p011.1 - p100.0 + p100.1 + p101.1 - 1\\p000.0 - 2 p000.1 - p001.0 - p001.1 - p010.0 - 2 p011.1 - p100.0 - p110.0 - p111.1\\- p000.1 - p001.0 - p010.0 - p011.1 - p100.0 - p110.0\\- p001.0 - p010.0 + p010.1 - p100.0 + p100.1 + p101.1 + p111.1 - 1\\- p001.0 + p001.1 - p010.0 + p010.1 - p100.0 - p101.0 + 2 p101.1 - p110.0 + p111.0 - 1\\p000.0 - p001.0 + p001.1 - p010.0 + 2 p010.1 + 2 p101.1 + 2 p111.0 - 2\\p000.0 - p000.1 - p001.0 - p010.0 + p010.1 - p011.1 + p101.1 + p111.0 - 1\\p000.0 - p000.1 - p001.0 - p010.0 + p010.1 - p011.1 + p101.1 - p110.0 + p110.1 - 1\\- p001.0 - p010.0 + p010.1 + p101.1 - p110.0 + p110.1 + p111.1 - 1\\- p001.0 - p010.0 + p010.1 + p101.1 + p111.1 - 1\\- p001.0 + p001.1 - p010.0 + p010.1 - p100.0 + p101.1 - p110.0 + p111.0 - 1\\- p001.0 - p010.0 + p010.1 + p101.1 + p111.0 - 1\\p000.0 - p000.1 - p001.0 - p011.1 - p100.0 + p100.1 + p101.1 - p110.0 + p110.1 - 1\\p000.0 - p000.1 - p001.0 - p011.1 - p100.0 + p100.1 + p101.1 - 1\\- p001.0 - p001.1 + p010.0 - p010.1 - p100.0 + p100.1 - p110.0 + p110.1 + p111.1 - 1\\- p001.0 - p001.1 + p010.0 - p010.1 - p100.0 + p100.1 + p111.1 - 1\\- p001.0 - p100.0 + p100.1 + p101.1 - p110.0 + p110.1 + p111.1 - 1\\- p001.0 - p100.0 + p100.1 + p101.1 + p111.1 - 1\\- p001.0 + p001.1 - p010.0 + p011.0 - p100.0 - p101.0 + 2 p101.1 - p110.0 + p111.1 - 1\\- p000.0 - 2 p001.0 + p001.1 - 2 p010.0 - 2 p100.0 - 2 p101.0 + 2 p101.1 - 2 p110.0 + p110.1 - 2 p111.0 + p111.1\\- p000.0 - 3 p001.0 + p001.1 - 2 p010.0 - 2 p100.0 - 2 p101.0 + 2 p101.1 - 3 p110.0 + 2 p110.1 - 3 p111.0 + p111.1\\p000.0 + p001.1 + p010.1 + p011.0 + 2 p101.1 + p111.0 + p111.1 - 2\\p000.0 - 2 p000.1 - p001.0 - p001.1 - p010.0 - 2 p011.1 - 2 p100.1 - 2 p110.1 + p111.0 - p111.1\\- p000.0 + p000.1 - 2 p010.0 + p011.1 - 2 p100.0 - 2 p101.0 + 3 p101.1 - 2 p110.0 - p111.0 + 2 p111.1 - 1\\- p010.0 + p011.0 - p100.0 - p101.0 + 2 p101.1 - p110.0 + p111.1 - 1\\- p000.0 + p000.1 + p011.1 - p100.0 + p101.1 - p110.0 - p111.0 + 2 p111.1 - 1\\- p001.1 + p010.0 - p010.1 + p011.0 + p101.0 + p111.1 - 1\\p001.0 + p010.0 + 2 p011.0 + 2 p101.0 + 2 p111.1 - 2\\p001.0 + p010.0 + 2 p011.0 + p101.0 + p101.1 + 2 p111.1 - 2\\p000.1 + p001.0 + p011.0 + p011.1 + 2 p101.1 + 2 p111.1 - 2\\- p000.0 - 2 p001.0 + p001.1 - 2 p010.0 - 2 p100.0 - 2 p110.0 - p111.0 + p111.1\\p011.0 + p101.0 + p111.1 - 1\\p011.0 + p101.1 + p111.1 - 1\\- p001.0 - p001.1 + p010.0 - p010.1 - p110.0 + p110.1 + p111.1 - 1\\p010.0 + 2 p011.0 + p101.0 + p101.1 + p110.1 - p111.0 + 2 p111.1 - 2\\- p001.0 + p001.1 - p010.0 + p011.0 - p100.0 + p101.1 - p110.0 + p110.1 - p111.0 + p111.1 - 1\\- p001.0 + p011.0 + p101.1 - p110.0 + p110.1 - p111.0 + p111.1 - 1\\- p001.0 + p101.1 - p110.0 + p110.1 + p111.1 - 1\\- p000.1 - p001.0 - p010.0 - p011.1 - p100.0 - p100.1 - p110.0 - p110.1\\- p001.0 - p010.0 + p010.1 + p101.1 + p111.1 - 1
\end{matrix}\right\}

Upper bound

\min\left\{\begin{matrix}
p000.1 - p001.0 + p001.1 + p010.1 + p100.0 + 2 p101.1 - p110.0 + 2 p110.1 + p111.1\\p000.1 - p001.0 + p001.1 + p010.1 + p100.0 + p101.1 + p110.1 + p111.1\\p000.0 + p000.1 - p001.0 + p001.1 + p010.0 + p010.1 + p100.0 + p101.1 + p110.1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 + p010.1 + p011.1 + p100.0 + 2 p101.1 - p110.0 + 2 p110.1 + 2 p111.1\\p000.1 - p001.0 + p001.1 - p010.0 + 2 p010.1 + p011.1 + p100.0 + 2 p101.1 - p110.0 + 2 p110.1 + 2 p111.1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 - p010.0 + 2 p010.1 + p011.1 + p100.0 + 2 p101.1 + p110.1 + 2 p111.1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 + p010.1 + p011.1 + p100.0 + 2 p101.1 + p110.1 + 2 p111.1\\p000.1 - p001.0 + p001.1 - p010.0 + 2 p010.1 + p011.1 + p100.0 + 2 p101.1 + p110.1 + 2 p111.1\\p000.0 + p000.1 - 2 p001.0 + p001.1 + p010.0 + p010.1 - p011.0 + p101.0 - p101.1 + p110.0 + p110.1 - p111.0 + 1\\p000.1 - 2 p001.0 + p001.1 + p010.1 - p011.0 + p110.1 - p111.0 + 1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 - p010.0 + 2 p010.1 + p011.1 + p100.0 + 2 p101.1 - p110.0 + 2 p110.1 + 2 p111.1\\p000.0 + p001.1 + p010.1 + p100.0 + p101.0 + 2 p101.1 - p110.0 + 2 p110.1 + p111.1\\p000.1 + p001.1 + p010.0 + p100.0 + p101.0 + 2 p101.1 - p110.0 + 2 p110.1 + p111.1\\- p001.0 + p001.1 - p011.0 + 2 p101.1 - 2 p110.0 + 2 p110.1 - p111.0 + p111.1 + 1\\p000.1 - 2 p001.1 + p010.1 - 2 p011.0 - p100.0 - 2 p101.0 + p101.1 + p110.1 - 2 p111.0 + 2\\p000.0 + p010.1 + p100.0 + p101.0 + p101.1 + p110.1 + p111.1\\- p001.0 - p011.0 + p101.1 - p110.0 + p110.1 - p111.0 + 1\\p000.1 + p010.0 + p100.0 + p101.0 + p101.1 + p110.1 + p111.1\\p000.1 + p010.1 + p100.0 + p101.1 + p110.1 + p111.1\\p000.1 - p001.1 + p010.1 - p011.0 - p101.0 + p101.1 + p110.1 - p111.0 + 1\\p000.0 + p000.1 + p010.0 + p010.1 + p100.0 + p101.1 + p110.1\\p000.1 - 2 p001.0 + p001.1 + p010.1 - p011.1 - p101.0 + p101.1 - p110.0 + p110.1 - p111.0 + 1\\2 p000.1 - 3 p001.0 + 2 p001.1 + 2 p010.1 - p011.0 - p100.0 + p100.1 + 2 p110.1 - 2 p111.0 + p111.1 + 1\\p000.1 - 2 p001.0 + p001.1 + p010.1 - p011.1 + p110.1 - p111.0 + 1\\p000.0 + p001.1 + p010.0 + p100.1 + p101.0 + 2 p101.1 - p110.0 + 2 p110.1 + p111.1\\p000.0 + p001.1 + p010.1 + p100.1 + p101.0 + 2 p101.1 - p110.0 + 2 p110.1 + p111.1\\p000.1 - p001.0 + p010.1 - p011.1 - p101.0 + p101.1 - p110.0 + p110.1 - p111.0 + 1\\- p001.0 - p011.1 + p101.1 - p110.0 + p110.1 - p111.0 + 1\\- 2 p001.0 - 2 p011.1 - p101.0 - p110.0 - 2 p111.0 + 2\\- p001.0 - p001.1 - 2 p011.1 - p101.0 - p110.0 - 2 p111.0 + 2\\- 2 p001.1 - p011.0 - p011.1 - p100.0 - p101.1 - 2 p111.0 + 2\\- 2 p001.1 - p011.0 - p011.1 - p100.0 - p101.0 - 2 p111.0 + 2\\p000.1 - 2 p001.1 + p010.1 - p011.0 - p011.1 - p100.0 - 2 p101.0 + p101.1 + p110.1 - 2 p111.0 + 2\\p000.0 + p010.0 + p100.1 + p101.0 + p101.1 + p110.1 + p111.1\\p000.0 + p010.1 + p100.1 + p101.0 + p101.1 + p110.1 + p111.1\\2 p000.1 + 2 p010.1 + p100.1 - p101.0 + 2 p101.1 + 2 p110.1 - p111.0 + p111.1\\- p001.1 - p011.1 - p111.0 + 1\\- 2 p001.0 - p011.0 - p011.1 - p100.0 - p101.1 - 2 p111.0 + 2\\- p001.0 - p011.1 - p111.0 + 1\\p000.1 + p001.1 + p010.0 + p100.1 + p101.0 + 2 p101.1 - p110.0 + 2 p110.1 + p111.1\\p000.1 - p001.0 + p011.0 - p011.1 + p100.1 + p101.1 - p110.0 + p110.1 - 2 p111.0 + p111.1 + 1\\- p000.0 + 2 p000.1 - p001.0 + p011.1 - 2 p100.0 + 2 p100.1 + p101.1 - p110.0 + 2 p110.1 - 3 p111.0 + 2 p111.1 + 1\\p000.1 - p001.1 - p100.0 + p100.1 + p110.1 - 2 p111.0 + p111.1 + 1\\p000.1 + p010.0 + p011.0 + p100.1 + p101.0 + p101.1 + p110.1 - p111.0 + p111.1\\p000.1 - p001.0 - p100.0 + p100.1 + p110.1 - 2 p111.0 + p111.1 + 1\\p000.1 + p010.0 + p100.1 + p101.0 + p101.1 + p110.1 + p111.1\\p000.0 + p010.0 + p011.1 - p100.0 + 2 p100.1 + p101.0 + p101.1 + p110.1 + 2 p111.1\\p000.0 + p010.1 + p011.1 - p100.0 + 2 p100.1 + p101.0 + p101.1 + p110.1 + 2 p111.1\\- 2 p001.1 - p011.0 - p011.1 - p100.0 - p101.1 - p110.1 - p111.0 + 2\\- 2 p001.1 - p011.0 - p011.1 - p100.0 + p101.0 - p101.1 + p110.0 - 2 p110.1 + 2\\- p001.1 - p011.1 + p101.0 + p110.0 - p110.1 + 1\\p000.0 + p000.1 + p010.0 + p010.1 + p100.1 + p101.0 + p110.0 + p111.1\\3 p000.1 - p001.0 + 2 p001.1 + 2 p010.1 - p011.0 + 3 p011.1 + 3 p100.1 + 3 p101.1 - p110.0 + 3 p110.1 - p111.0 + 2 p111.1 - 1\\- p001.0 - p001.1 - 2 p011.0 - p100.0 - p101.1 - p110.1 - p111.0 + 2\\- p001.1 - p011.0 + p101.0 + p110.0 - p110.1 + 1\\- p001.0 - p011.0 + p011.1 - 2 p100.0 + 2 p100.1 + p101.1 - p111.0 + 2 p111.1 + 1\\p000.1 + p010.0 + p011.1 - p100.0 + 2 p100.1 + p101.0 + p101.1 + p110.0 + 2 p111.1\\- p001.1 - p011.0 - p100.0 + p100.1 + p101.0 + p110.0 - p110.1 + p111.1 + 1\\- 2 p001.1 - 2 p011.0 - p100.0 + p101.0 - p101.1 + p110.0 - 2 p110.1 + 2\\- 2 p001.1 - 2 p011.0 - p100.0 - p101.1 - p110.1 - p111.0 + 2\\p000.0 + p010.1 + p011.1 - p100.0 + 2 p100.1 + p101.0 + p101.1 + p110.0 + 2 p111.1\\p000.1 + p010.1 + p100.1 + p101.0 + p101.1 + p110.0 + p111.1\\p000.1 + p010.0 + p100.1 + p101.0 + p101.1 + p110.0 + p111.1\\- p001.0 - p011.0 - p100.0 + p100.1 - p111.0 + p111.1 + 1\\p000.0 + p010.1 + p100.1 + p101.0 + p101.1 + p110.0 + p111.1\\- p001.1 - p011.0 - p100.0 + p100.1 - p111.0 + p111.1 + 1\\p000.1 + p010.0 + p011.1 - p100.0 + 2 p100.1 + p101.0 + p101.1 + p110.1 - p111.0 + 2 p111.1\\p000.1 + p010.0 + p011.1 + p100.1 + p101.0 + p101.1 + p110.1 - p111.0 + p111.1\\p000.1 - p001.0 - p011.0 + p011.1 - p100.0 + p100.1 + p110.1 - 2 p111.0 + p111.1 + 1\\p000.1 - p001.1 - p011.0 + p011.1 - p100.0 + p100.1 + p110.1 - 2 p111.0 + p111.1 + 1\\2 p000.1 + p010.0 + 2 p011.1 - p100.0 + 2 p100.1 + p101.0 + p101.1 + 2 p110.1 - 2 p111.0 + 2 p111.1\\- p000.0 + p000.1 - p001.0 - p011.0 + p101.1 - p111.0 + p111.1 + 1\\p000.1 + p010.1 + p100.0 + p101.0 + p101.1 + p110.0 + p111.1\\- p001.0 - p011.0 - p111.0 + 1\\- 2 p001.0 - 2 p011.0 - p100.0 - p101.1 - 2 p111.0 + 2\\- p001.1 - p011.0 - p111.0 + 1\\p000.1 - 2 p001.0 + p001.1 + p010.1 - 2 p011.0 + p011.1 + p100.1 - p101.0 + p101.1 - p110.0 + p110.1 - p111.0 + 1\\p000.0 + p000.1 + p010.0 + p010.1 - p011.0 + p011.1 + p100.0 + p100.1 + p101.1 + p110.1\\- p001.0 - p010.0 + p010.1 - p011.0 + p101.1 - p111.0 + p111.1 + 1\\- 2 p001.1 - 2 p011.0 - p100.0 - p101.0 - 2 p111.0 + 2\\- 2 p001.1 - 2 p011.0 - p100.0 - p101.1 - 2 p111.0 + 2
\end{matrix}\right\}

4. Sharp bounds of $\bar{\xi}(0)$ (NDE(0))

Lower bound

\max\left\{\begin{matrix}
p000.1 + p010.0 + p101.0 - p101.1 - p110.1 - 1\\p000.1 - p011.0 + p011.1 - p100.0 + p101.0 - p101.1 - p110.0 - p110.1 - 1\\p000.1 - p001.1 + p010.0 - p011.1 + p101.0 - p101.1 + p110.0 - p110.1 - 1\\p000.1 - p001.0 + p001.1 - p100.0 + p101.0 - p101.1 - p110.0 - p110.1 - 1\\p000.0 + p010.0 - p010.1 - p100.1 + 2 p101.0 - 2 p101.1 - 2 p110.1 + p111.0 - p111.1 - 1\\p000.0 + p010.0 - p010.1 + p011.0 - p011.1 - p100.1 + 2 p101.0 - 2 p101.1 - 2 p110.1 - 1\\p000.0 + p001.0 - p001.1 + p010.0 - p010.1 - p100.1 + 2 p101.0 - 2 p101.1 - 2 p110.1 - 1\\p000.1 - p001.1 + 2 p010.0 - p010.1 - p011.1 + p101.0 - p101.1 + p110.0 - p110.1 - 1\\- p001.1 + p010.0 - p010.1 - p011.1 - p100.0 - p100.1 + p101.0 - 2 p101.1 - 2 p110.1 - p111.0\\- 2 p001.1 + 2 p010.0 - 2 p010.1 - 2 p011.1 + p100.0 - 2 p100.1 + p101.0 - 2 p101.1 + p110.0 - 2 p110.1 - 2 p111.1\\- 2 p001.1 + p010.0 - p010.1 - 2 p011.1 + p100.0 - 2 p100.1 + p101.0 - 2 p101.1 + p110.0 - 2 p110.1 - 2 p111.1\\- 3 p001.1 + p010.0 - p010.1 - 3 p011.1 + 2 p100.0 - 3 p100.1 + p101.0 - 2 p101.1 + p110.0 - 2 p110.1 - 3 p111.1\\- 3 p001.1 + 2 p010.0 - 2 p010.1 - 3 p011.1 + 2 p100.0 - 3 p100.1 + p101.0 - 2 p101.1 + p110.0 - 2 p110.1 - 3 p111.1\\p000.0 + p010.0 - p010.1 - p100.1 + 2 p101.0 - 2 p101.1 - 2 p110.1 - 1\\p000.0 + p010.1 - p100.1 - p101.0 + p101.1 - p110.0 + p111.0 - p111.1 - 1\\p000.0 - p001.0 + p010.1 - p100.1 - p101.0 + p101.1 - p110.0 + p110.1 - p111.1 - 1\\2 p000.0 + 2 p010.1 + p100.0 + p101.1 + p110.1 + p111.0 - 2\\2 p000.0 + 2 p010.1 + p100.0 - p100.1 + p101.1 + 2 p111.0 - p111.1 - 2\\p000.0 + p010.1 - p100.1 + p111.0 - p111.1 - 1\\p000.0 + p000.1 + 2 p010.1 + p100.0 + p101.1 + p110.1 + p111.0 - 2\\p010.1 - p011.0 + p011.1 - p100.0 - p100.1 - p101.0 + p101.1 - p110.0 + p111.0 - p111.1 - 1\\p010.1 - p011.0 + p011.1 - p100.0 - p100.1 - p110.0 + p111.0 - p111.1 - 1\\- p001.0 + p001.1 + p010.1 - p100.0 - p100.1 - p110.0 + p111.0 - p111.1 - 1\\- p001.0 + p001.1 + p010.1 - p100.0 - p100.1 - p101.0 + p101.1 - p110.0 + p111.0 - p111.1 - 1\\- p001.0 + p001.1 + p010.1 - p011.0 + p011.1 - p100.0 - p100.1 - p110.0 + p111.0 - p111.1 - 1\\- p000.1 - p001.0 - p011.1 - p100.0 - 2 p100.1 - p101.0 - p110.0 - 2 p111.1\\p000.1 - p001.0 - p010.0 + 2 p010.1 - p011.0 - p101.0 - 1\\p000.0 + p000.1 - p001.1 + 2 p010.1 - p011.1 + p100.0 - p101.1 + 2 p110.0 - p110.1 + p111.0 - 2\\- p000.1 - p001.0 - p011.0 - p100.0 - 2 p100.1 - p101.0 - p110.0 - p110.1 + p111.0 - 2 p111.1\\- p000.1 - p001.0 - p011.0 - p100.0 - 2 p100.1 - p101.0 - p110.0 - 2 p111.1\\2 p000.0 + 2 p010.1 + p100.0 + p110.0 + p111.0 - 2\\2 p000.0 - p001.1 + 2 p010.1 - p011.1 + p100.0 - p101.1 + 2 p110.0 - p110.1 + p111.0 - 2\\p000.1 - p010.0 + p010.1 - p011.0 + p011.1 - p100.0 - 2 p101.0 + 2 p101.1 - 2 p110.0 - 1\\p000.1 - p001.0 + p001.1 - p010.0 + p010.1 - p100.0 - 2 p101.0 + 2 p101.1 - 2 p110.0 - 1\\p000.0 + p011.0 - p011.1 - p100.1 - p101.0 + p101.1 - p110.0 - p111.1 - 1\\- 2 p001.0 - p010.0 - p011.1 - p100.0 - p100.1 - 2 p101.0 + p101.1 - 2 p110.0 + p110.1 - 2 p111.0 - p111.1\\2 p000.0 - 2 p000.1 - 2 p001.1 - 3 p011.1 + p100.0 - 3 p100.1 - p101.1 - 3 p110.1 + p111.0 - 2 p111.1\\2 p000.0 - 2 p000.1 - 2 p001.1 - 2 p011.1 + p100.0 - 2 p100.1 - p101.1 - 2 p110.1 + p111.0 - 2 p111.1\\p000.0 - p000.1 - p001.1 - 2 p011.1 - 2 p100.1 - p101.0 - p110.0 - 2 p110.1 - p111.1\\p000.0 + p010.1 - p101.0 + p101.1 - p110.0 - 1\\2 p000.0 + p010.0 + p010.1 + p100.0 + p101.1 + p110.1 + p111.0 - 2\\2 p000.0 - 2 p000.1 - 2 p001.1 - 3 p011.1 + p100.0 - 3 p100.1 - p101.1 - 3 p110.1 + 2 p111.0 - 3 p111.1\\p000.0 - p000.1 - p001.1 - 2 p011.1 - 2 p100.1 - p101.0 - p110.0 - 2 p110.1 + p111.0 - 2 p111.1\\2 p000.0 + p010.0 + p010.1 + p011.0 + p100.0 + p101.1 + p110.1 - 2\\2 p000.0 + p010.0 + 2 p011.0 - p011.1 + p100.0 - p100.1 + p101.1 + p110.1 - p111.0 - 2\\p000.0 + p011.0 - p011.1 - p100.1 - p101.0 + p101.1 - p110.0 - p111.0 - 1\\p000.0 + p011.0 - p011.1 - p100.1 - p101.0 + p101.1 - p110.0 - p110.1 - 1\\p000.0 + p001.0 - p001.1 - p100.1 - p101.0 + p101.1 - p110.0 - p110.1 - 1\\p000.0 + p001.0 - p001.1 + p011.0 - p011.1 - p100.1 - p101.0 + p101.1 - p110.0 - p110.1 - 1\\p000.1 - p010.0 + p010.1 - p100.0 - 2 p101.0 + 2 p101.1 - 2 p110.0 - 1\\2 p000.0 - p000.1 - p001.1 + p010.0 - p011.1 - p111.1 - 1\\3 p000.0 - 2 p000.1 - 2 p001.1 + 2 p010.0 - p010.1 - 2 p011.1 + p101.0 - p101.1 + p110.0 - p110.1 - 2 p111.1 - 1\\2 p000.0 - p000.1 - p001.1 + p010.1 - p011.1 - p111.1 - 1\\3 p000.0 - 2 p000.1 - 2 p001.1 + p010.0 - 2 p011.1 + p101.0 - p101.1 + p110.0 - p110.1 - 2 p111.1 - 1\\- p001.1 - p011.0 - p100.0 - p100.1 - p101.0 - p110.0 - p110.1 - p111.1\\p000.1 + p010.1 - p011.0 + p011.1 - p100.0 - p110.0 - 1\\- p001.0 - p011.1 - p100.0 - p100.1 - p101.0 - p110.0 - p110.1 - p111.1\\p000.1 - p001.0 + p001.1 + p010.1 - p100.0 - p110.0 - 1\\p000.0 + p010.0 + p011.0 - p011.1 - p100.1 - p111.1 - 1\\p000.0 + p010.0 - p100.1 + p111.0 - p111.1 - 1\\p000.1 + p010.0 - 1\\p000.1 + p010.1 - p101.0 + p101.1 - p110.0 - 1\\p000.1 + p010.1 - 1\\- 2 p001.1 - 2 p011.1 - p100.1 - 2 p101.1 + p110.0 - 2 p110.1 - p111.1\\- 2 p001.1 - 2 p011.1 + p100.0 - 2 p100.1 - p101.1 - p110.1 - 2 p111.1\\p000.1 - p001.1 + p010.0 - p011.1 + p100.0 - p100.1 - p111.1 - 1\\- p001.0 - p001.1 - p011.1 - p100.1 - p101.0 - p110.0 - p111.0 - p111.1\\- p001.0 - p011.0 - p100.0 - p100.1 - p101.1 - p110.0 - p110.1 - p111.1\\p000.0 + p000.1 + 2 p010.0 + p100.0 + p110.1 + p111.0 - 2\\- p001.0 - p001.1 - p011.0 - p011.1 - p100.1 - p101.0 - p110.0 - p111.1\\p000.0 - p001.1 + p010.0 - p011.1 + p101.0 - p101.1 + p110.0 - p110.1 - 1\\p000.0 - p001.1 + p010.1 - p011.1 - p101.1 + p110.0 - p110.1 - 1\\2 p000.0 - p000.1 - p001.1 + p010.0 - p011.1 + p101.0 - p101.1 + p110.0 - p110.1 - p111.1 - 1\\p000.0 - p000.1 - p001.1 - 2 p011.1 - 2 p100.1 - p101.1 - 2 p110.1 - p111.1\\p000.0 + p010.1 - 1\\2 p000.0 - p000.1 - p001.1 + 2 p010.0 - p010.1 - p011.1 + p101.0 - p101.1 + p110.0 - p110.1 - p111.1 - 1\\p000.0 + p010.0 - 1\\p000.0 + p010.0 + p101.0 - p101.1 - p110.1 - 1\\2 p000.0 + 2 p010.0 + p100.0 + p110.1 + p111.0 - 2\\p000.0 - p001.1 + p010.1 - p011.1 + p100.0 - p100.1 - p110.1 + p111.0 - p111.1 - 1\\p000.0 + p010.1 - p011.1 - p100.1 - p110.1 + p111.0 - p111.1 - 1\\p000.0 + p001.0 - p001.1 + p010.0 + p011.0 - p011.1 - p100.1 - p110.1 - 1\\p000.0 + p010.0 + p011.0 - p011.1 - p100.1 - p111.0 - 1\\p000.0 + p010.0 + p011.0 - p011.1 - p100.1 - p110.1 - 1\\p000.0 + p010.0 + p011.0 - p011.1 - p100.1 + p101.0 - p101.1 - p110.1 - 1\\p000.0 + p001.0 - p001.1 + p010.0 - p100.1 - p110.1 - 1\\p000.0 + p001.0 - p001.1 + p010.0 - p100.1 + p101.0 - p101.1 - p110.1 - 1\\- p001.1 - p011.1 - p100.0 - p100.1 - p101.1 - p110.1 - p111.0\\p000.0 - p000.1 + 2 p001.0 - 2 p001.1 + 2 p010.0 - p010.1 + 2 p011.0 - 2 p011.1 - 2 p100.1 + 2 p101.0 - 2 p101.1 + p110.0 - 2 p110.1 - 1\\p000.0 - p001.1 + 2 p010.0 - p010.1 - p011.1 - p101.1 - 1\\2 p000.0 - p001.1 + 3 p010.0 - p010.1 - p011.1 + p100.0 - p101.1 + p110.1 + p111.0 - 2\\p000.0 - 2 p001.1 + 3 p010.0 - 2 p010.1 - 2 p011.1 + p100.0 - p100.1 - 2 p101.1 + p111.0 - p111.1 - 1\\p000.1 - p001.1 + 2 p010.0 - p010.1 - p011.1 - p101.1 - 1\\- p000.1 - p001.1 + p010.0 - p010.1 + p011.0 - 2 p011.1 - p100.0 - 2 p100.1 - p101.1 - p110.1 - 2 p111.0\\- p000.1 - p001.1 + p010.0 - p010.1 + p011.0 - 2 p011.1 - p100.0 - 2 p100.1 - p101.1 - 2 p110.1 - p111.0\\- p000.1 - p001.1 + p010.0 - p010.1 + p011.0 - 2 p011.1 - p100.0 - 2 p100.1 + p101.0 - 2 p101.1 - 2 p110.1 - p111.0\\- p000.1 + p001.0 - 2 p001.1 + p010.0 - p010.1 - p011.1 - p100.0 - 2 p100.1 - p101.1 - 2 p110.1 - p111.0\\- p000.1 + p001.0 - 2 p001.1 + p010.0 - p010.1 - p011.1 - p100.0 - 2 p100.1 + p101.0 - 2 p101.1 - 2 p110.1 - p111.0\\- p000.1 + p001.0 - 2 p001.1 + p010.0 - p010.1 + p011.0 - 2 p011.1 - p100.0 - 2 p100.1 - p101.1 - 2 p110.1 - p111.0\\p000.0 - p001.1 + 2 p010.0 - p010.1 - p011.1 + p101.0 - p101.1 + p110.0 - p110.1 - 1\\- p001.1 + p010.0 - p010.1 - p011.1 - p100.0 - p100.1 - p101.1 - p110.1 - p111.0
\end{matrix}\right\}

Upper bound

\min\left\{\begin{matrix}
p000.1 + p001.0 - p001.1 + p010.0 + p011.0 - p100.0 - p111.0 + p111.1 + 1\\p000.1 + p001.0 - p001.1 + p010.0 + p010.1 - p100.0 - p111.0 + p111.1 + 1\\p000.0 + 2 p001.0 - 2 p001.1 + 2 p010.0 - p100.1 + p101.0 - p101.1 + p110.0 - p110.1 + 1\\p000.1 + p001.0 - p001.1 + p010.0 + p011.1 - p100.0 - p111.0 + p111.1 + 1\\- p000.0 + 2 p000.1 + p011.0 + p011.1 - 2 p100.0 + p100.1 + p101.1 - p110.0 + p110.1 - 2 p111.0 + 2 p111.1 + 1\\- p000.0 + 2 p000.1 + 2 p011.1 - 2 p100.0 + p100.1 + p101.1 - p110.0 + p110.1 - 2 p111.0 + 2 p111.1 + 1\\p000.0 + 2 p001.0 - 2 p001.1 + 2 p010.0 - p100.1 + 2 p101.0 - p101.1 + 2 p110.0 - 3 p110.1 + 2 p111.0 + 1\\p000.1 + p001.0 - p001.1 + p010.0 + p010.1 - p100.0 + p101.0 + p110.0 - 2 p110.1 + p111.0 + p111.1 + 1\\p001.0 - 2 p001.1 + p010.0 - p011.0 - p100.0 - p100.1 - p101.1 - 2 p110.1 + 2\\p000.1 + p001.0 - p001.1 + p010.0 + p010.1 - p100.0 - p110.1 + p111.1 + 1\\p000.0 + 2 p001.0 - 2 p001.1 + 2 p010.0 + p011.0 - p011.1 - p100.1 + p110.0 - p110.1 + 1\\p000.1 + p001.0 - p001.1 + p010.0 + p010.1 - p011.0 + p011.1 - p100.0 - p101.0 + p101.1 + 1\\p000.1 + p001.0 - p001.1 + p010.0 + p010.1 - p100.0 - p101.0 + p101.1 + 1\\- p000.0 + p000.1 - p011.0 + p011.1 - 2 p100.0 + p100.1 + p101.1 - p110.0 + p111.1 + 1\\- p000.0 - p001.1 - p011.0 - 2 p100.0 - 2 p110.1 + 2\\- p000.0 + p000.1 + p011.1 - 2 p100.0 + p100.1 + p101.1 - p110.0 - p111.0 + p111.1 + 1\\p001.0 - p001.1 + p010.0 - p100.0 - p110.1 + 1\\p011.1 - 2 p100.0 + p100.1 + p101.1 - p110.1 + p111.1 + 1\\- p001.0 + p001.1 - p010.0 + p010.1 + 2 p011.1 - 3 p100.0 + 2 p100.1 + 2 p101.1 - p110.0 + 2 p111.1 + 1\\p011.1 - 2 p100.0 + p100.1 + p101.1 - p110.0 + p111.1 + 1\\- p001.0 + p001.1 - p010.0 + p010.1 + 2 p011.1 - 3 p100.0 + 2 p100.1 + 2 p101.1 - 2 p110.0 + p110.1 + 2 p111.1 + 1\\p000.0 + 2 p001.0 - 2 p001.1 + 2 p010.0 - p100.1 + p110.0 - p110.1 + 1\\- p000.0 + p000.1 - p011.0 + p011.1 - p100.0 + p101.1 - p110.0 + p111.1 + 1\\- p000.0 + p000.1 + p011.1 - p100.1 + p101.1 - p110.0 + p111.1 + 1\\- p001.0 + p001.1 - p010.0 + p010.1 - p100.0 + p101.1 - p110.0 + p111.1 + 1\\- p000.0 - p001.1 - p011.0 - p100.0 - p100.1 - 2 p110.1 + 2\\- p001.1 - p011.0 - p100.0 - p100.1 - p101.1 - 2 p110.1 + 2\\p000.1 + p010.1 - p100.0 - p110.1 + p111.1 + 1\\- p000.0 + p000.1 + p011.1 - p100.0 + p101.1 - p110.0 - p111.0 + p111.1 + 1\\p000.1 + p011.1 - p100.0 - p110.0 - p111.0 + p111.1 + 1\\p000.0 + p000.1 + p001.0 + p010.0 + p010.1 + p011.1 + p101.0 + p111.1\\p000.1 + p010.1 - p100.0 - p110.0 - p111.0 + p111.1 + 1\\p000.1 + p011.0 - p100.0 - p110.0 - p111.0 + p111.1 + 1\\p001.1 - p010.0 + p010.1 - p100.0 + p101.1 - p110.1 + p111.1 + 1\\p000.1 + 2 p001.1 - p010.0 + 2 p010.1 + p011.1 + 2 p101.1 + 2 p111.1\\- p000.0 + 2 p000.1 + p001.1 + p010.1 + 2 p011.1 + 2 p101.1 + 2 p111.1\\p000.0 + p000.1 + p001.0 + p010.0 + p010.1 + p011.0 + p101.1 + p111.1\\p000.0 + p011.0 - p011.1 - p100.1 - p110.1 + 1\\- p100.1 - p110.1 + 1\\p000.0 + p010.0 - p100.1 + p101.0 - p101.1 - p110.1 + 1\\p000.0 + p000.1 + p001.1 + p010.0 + p010.1 + p011.0 + p101.0 + p111.1\\p001.0 - p001.1 + p010.0 - p100.1 - p110.1 + 1\\- p001.0 + p001.1 - p010.0 + p010.1 + p011.1 - 2 p100.0 + p100.1 + p101.1 - p110.0 + p111.1 + 1\\- p100.0 - p110.1 + 1\\- p000.0 + p000.1 + p001.1 - p011.0 + p011.1 - p100.0 + p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\- p100.1 - p110.0 + 1\\p000.0 + p000.1 + p001.1 + p010.0 + p010.1 + p011.1 + p101.1 + p111.0\\- p000.0 + p000.1 + p001.1 - p011.0 + p011.1 - 2 p100.0 + p100.1 + p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\- p001.0 + p001.1 - p010.0 + p010.1 + p011.1 - 2 p100.0 + p100.1 + p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\- p100.0 - p110.0 + 1\\p000.1 - p011.0 + p011.1 - p100.0 - p110.0 + 1\\p000.1 - p001.0 + p001.1 + p010.1 - p011.0 + p011.1 - p100.0 - p110.0 + 1\\p000.1 - p001.0 + p001.1 + p010.1 - p100.0 - p101.0 + p101.1 - p110.0 + 1\\p000.1 + p010.1 - p011.0 + p011.1 - p100.0 - p101.0 + p101.1 - p110.0 + 1\\- p001.0 + p001.1 + p010.1 - p100.0 - p110.0 + 1\\p000.1 + p010.1 - p100.0 - p101.0 + p101.1 - p110.0 + 1\\2 p000.0 + p010.0 + 2 p011.0 - 2 p011.1 + p100.0 - p100.1 - p110.1 + 1\\- p000.0 + p000.1 + 2 p001.1 - p011.0 + p011.1 - p100.0 + 2 p101.1 - 3 p110.0 + 2 p110.1 + 2 p111.1 + 1\\p001.1 - p100.1 + p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\- p000.0 + p000.1 + 2 p001.1 - p011.0 + p011.1 - 2 p100.0 + p100.1 + 2 p101.1 - 3 p110.0 + 2 p110.1 + 2 p111.1 + 1\\p001.1 - p100.0 + p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.0 + p000.1 + p010.1 + p011.0 - p011.1 - p110.0 - p111.0 + p111.1 + 1\\p000.0 + p000.1 + 2 p011.0 - p011.1 - p110.0 - p111.0 + p111.1 + 1\\2 p000.0 + p010.0 + 2 p011.0 - 2 p011.1 + p100.0 - p100.1 + p101.0 - p101.1 - p110.1 + 1\\2 p000.0 + p001.0 - p001.1 + p010.0 + 2 p011.0 - 2 p011.1 + p100.0 - p100.1 - p110.1 + 1\\p000.0 + p000.1 - p001.0 + p001.1 + p010.1 + p011.0 - p011.1 - p101.0 + p101.1 - p110.0 + 1\\p000.0 + p011.0 - p011.1 - p100.1 - p110.0 + 1\\- p001.0 + p001.1 - p010.0 + p010.1 - p100.0 + p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.0 + p000.1 + p010.1 + p011.0 - p011.1 - p101.0 + p101.1 - p110.0 + 1\\- 2 p000.0 + 3 p000.1 - p001.0 + 2 p001.1 - p010.0 + 2 p010.1 + 3 p011.1 + 3 p101.1 - 2 p110.0 + 2 p110.1 + 3 p111.1\\- 2 p000.0 + 3 p000.1 - p001.0 + 2 p001.1 - p010.0 + 2 p010.1 + 3 p011.1 + 3 p101.1 - p110.0 + p110.1 + 3 p111.1\\- p000.0 + 2 p000.1 - p001.0 + 2 p001.1 - p010.0 + 2 p010.1 + 2 p011.1 + 2 p101.1 - p110.0 + p110.1 + 2 p111.1\\- p000.0 + 2 p000.1 - p001.0 + 2 p001.1 - p010.0 + 2 p010.1 + 2 p011.1 + 2 p101.1 - 2 p110.0 + 2 p110.1 + 2 p111.1\\p000.1 - 2 p001.0 + 2 p001.1 + 2 p010.1 - p100.0 - p110.0 + p110.1 + 1\\p000.0 - p001.0 + p001.1 + p010.0 + p010.1 - p100.1 + p101.0 - p101.1 + 1\\p000.1 - 2 p001.0 + 2 p001.1 + 2 p010.1 - p100.0 - p110.0 + p110.1 - p111.0 + p111.1 + 1\\- p001.0 + p001.1 - p010.0 + p010.1 - p100.1 + p101.1 - p110.0 + p111.1 + 1\\p000.0 + p000.1 - p001.0 + 2 p001.1 + p010.0 + 2 p010.1 + p011.1 + p101.1 + p110.1 + p111.0\\p000.1 - 2 p001.0 + 2 p001.1 + 2 p010.1 - p100.0 - p101.0 + p101.1 - p110.0 + p110.1 + 1\\- p001.0 + p001.1 + p010.1 - p100.1 - p110.0 + 1\\p000.1 - 2 p001.0 + 2 p001.1 + 2 p010.1 - p011.0 + p011.1 - p100.0 - p110.0 + p110.1 + 1\\- p001.0 + p001.1 - p010.0 + p010.1 - p100.1 + p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.0 - p001.0 + p001.1 + p010.1 + p011.0 - p011.1 - p100.1 - p110.0 + 1\\- p000.0 + 2 p000.1 + 3 p001.1 - 2 p010.0 + 3 p010.1 - p011.0 + 2 p011.1 - 2 p100.0 + 2 p100.1 + 3 p101.1 + 3 p111.1\\- p000.0 + 2 p000.1 + 3 p001.1 - 2 p010.0 + 3 p010.1 - p011.0 + 2 p011.1 - p100.0 + p100.1 + 3 p101.1 + 3 p111.1\\- p000.0 + 2 p000.1 + 2 p001.1 - p010.0 + 2 p010.1 - p011.0 + 2 p011.1 - p100.0 + p100.1 + 2 p101.1 + 2 p111.1\\- p000.0 + 2 p000.1 + 2 p001.1 - p010.0 + 2 p010.1 - p011.0 + 2 p011.1 - 2 p100.0 + 2 p100.1 + 2 p101.1 + 2 p111.1\\4 p000.1 + 2 p001.1 + 2 p010.1 - p011.0 + 4 p011.1 - p100.0 + 3 p100.1 + 2 p101.1 - p110.0 + 2 p110.1 + 2 p111.1 - 1\\2 p000.1 + p010.1 - 2 p011.0 + 2 p011.1 - p100.0 + p100.1 - p110.0 + 1\\2 p000.1 - p001.0 + p001.1 + p010.1 - 2 p011.0 + 2 p011.1 - p100.0 + p100.1 - p110.0 + 1\\2 p000.1 + p010.1 - 2 p011.0 + 2 p011.1 - p100.0 + p100.1 - p101.0 + p101.1 - p110.0 + 1\\p000.0 + 2 p000.1 + p001.1 + p010.0 + p010.1 - p011.0 + 2 p011.1 + p100.1 + p101.1 + p111.0\\p000.1 - p011.0 + p011.1 - p100.0 - p110.1 + 1\\- p000.0 + p000.1 - p011.0 + p011.1 - p100.0 + p101.1 - p110.1 + p111.1 + 1\\p000.0 + p000.1 + p010.0 - p011.0 + p011.1 + p101.0 - p101.1 - p110.1 + 1\\2 p000.1 + p010.1 - 2 p011.0 + 2 p011.1 - p100.0 + p100.1 - p110.0 - p111.0 + p111.1 + 1\\2 p000.1 - p011.0 + 2 p011.1 - p100.0 + p100.1 - p110.0 - p111.0 + p111.1 + 1\\p000.1 + p001.0 - p001.1 + p010.0 - p011.0 + p011.1 - p100.0 - p110.1 + 1\\- p000.0 + p000.1 - p011.0 + p011.1 - 2 p100.0 + p100.1 + p101.1 - p110.1 + p111.1 + 1\\2 p000.1 + p001.0 + p010.0 + 2 p011.1 - p100.0 + p100.1 + p101.0 + p101.1 + p111.1\\- p000.0 + p000.1 - p001.1 - 2 p011.0 + p011.1 - 2 p100.0 - 2 p110.1 + 2
\end{matrix}\right\}

Sharp bounds of population causal parameters under Assumptions 1--3, 5

1. Sharp bounds of $\bar{\delta}(1)$ (NIE(1))

Lower bound

\max\left\{\begin{matrix}
- p000.0 - p011.0 - p100.0 - p101.0 + p101.1\\- p000.0 + p000.1 + p001.1 + p010.0 - p011.0 + p101.1 + p110.0 - 1\\- p000.0 + p010.0 - p010.1 - p011.0 - p011.1 - p100.1 - p111.1\\- p000.0 - p011.0 - p011.1 - p100.1 + p110.0 - p110.1 - p111.1\\- p000.0 - p011.0 - p011.1 - p100.1\\- p000.0 - p011.0 - p100.0\\p001.1 + p010.0 + p101.1 + p110.0 + p111.0 - 1\\- p000.0 - p001.0 + p001.1 - p011.0 - p100.0\\- p000.1 - p011.1 - p100.1 + p101.0 - p101.1\\p001.1 + p010.1 + p101.0 + p110.0 - 1\\p001.1 + p010.0 + p101.0 + p110.1 - 1\\- p000.1 - p011.1 - p100.1\\p001.1 + p010.1 + p101.1 + p110.0 - 1\\p001.1 + p010.0 + p101.1 + p110.1 - 1\\p000.0 - p000.1 + p001.0 + p010.1 - p011.1 + p101.0 + p110.1 - 1\\- p000.1 - p011.0 - p011.1 - p100.0\\p000.0 - p000.1 + p001.0 + p010.1 - p011.1 + p101.0 + 2 p110.0 - p110.1 - p111.1 - 1\\- p000.1 - p011.0 - p011.1 - p100.0 + p110.0 - p110.1 - p111.1\\p000.0 - p000.1 + p001.0 + p010.1 - p011.1 + p101.0 + p110.0 - 1\\p001.1 + p010.0 - p011.0 - p100.0 + p100.1 + p101.1 + p110.0 - 1\\- p000.1 + p010.0 - p010.1 - p011.0 - p011.1 - p100.0 - p111.1\\p000.0 - p000.1 + p001.0 + 2 p010.0 - p010.1 - p011.1 + p101.0 + p110.1 - p111.1 - 1\\p000.0 - p000.1 + p001.0 + p010.0 - p011.1 + p101.0 + p110.1 - 1\\p001.0 + p010.1 + p101.0 + p110.1 + p111.1 - 1\\p001.0 + p010.1 + p101.0 + p110.0 - 1\\p001.0 + p010.0 + p101.0 + p110.1 - 1\\p001.0 + p010.1 - p011.1 + p100.0 - p100.1 + p101.0 + p110.1 - 1\\p001.0 + p010.1 - p011.1 + p100.0 - p100.1 + p101.0 + p110.0 - 1\\p001.0 + p010.1 - p011.1 + p100.0 - p100.1 + p101.0 + 2 p110.0 - p110.1 - p111.1 - 1\\p001.0 + p010.0 - p011.1 + p100.0 - p100.1 + p101.0 + p110.1 - 1\\p001.0 + 2 p010.0 - p010.1 - p011.1 + p100.0 - p100.1 + p101.0 + p110.1 - p111.1 - 1\\- p000.1 + p001.0 - p001.1 - p011.1 - p100.1\\p001.0 + p010.1 + p101.1 + p110.0 - 1\\p001.0 + p010.0 + p101.1 + p110.1 - 1
\end{matrix}\right\}

Upper bound

\min\left\{\begin{matrix}
- p001.1 - p010.0 - p011.0 - p101.1 - p110.0 + 1\\- p001.0 - p010.0 - p011.0 - p101.1 - p110.0 + 1\\- p001.1 - p010.0 - p011.0 - p101.0 - p110.0 + 1\\p000.0 + p100.0 + p111.0\\p000.0 - p010.0 + p010.1 + p011.1 + p100.1 - p110.0 + p110.1 + p111.0 + p111.1\\p000.1 - p010.0 + p010.1 + p011.1 + p100.0 - p110.0 + p110.1 + p111.0 + p111.1\\p000.0 + p011.1 + p100.1 - p110.0 + p110.1 + p111.0 + p111.1\\- p001.0 - p010.1 + p011.1 - p100.0 + p100.1 - p101.0 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.1 + p011.1 + p100.0 - p110.0 + p110.1 + p111.0 + p111.1\\- p000.0 + p000.1 - p001.0 - p010.1 + p011.1 - p101.0 - 2 p110.0 + p110.1 + p111.1 + 1\\- p001.1 - p010.1 - p101.1 - p110.0 + 1\\- p001.0 - p010.1 - p101.1 - p110.0 + 1\\- p001.1 - p010.1 - p101.0 - p110.0 + 1\\- p001.0 - p010.1 - p101.0 - p110.0 + 1\\- p001.1 - p010.0 - p101.1 - p110.1 + 1\\- p001.0 - p010.0 - p101.1 - p110.1 + 1\\- p001.1 - p010.0 - p101.0 - p110.1 + 1\\- p001.0 - p010.0 - p101.0 - p110.1 + 1\\p000.0 - p010.0 + p010.1 + p011.1 + p100.1 + p111.0 + p111.1\\p000.1 - p010.0 + p010.1 + p011.1 + p100.0 + p111.0 + p111.1\\- p001.0 - 2 p010.0 + p010.1 + p011.1 - p100.0 + p100.1 - p101.0 - p110.1 + p111.1 + 1\\- p000.0 + p000.1 - p001.0 - 2 p010.0 + p010.1 + p011.1 - p101.0 - p110.1 + p111.1 + 1\\p000.1 + p100.1 + p111.1\\p000.1 - p001.0 + p001.1 + p100.1 + p111.1\\p000.1 + p100.1 - p101.0 + p101.1 + p111.1\\- p001.0 - p010.1 - p011.1 - p101.0 - p110.1 + 1\\- p001.0 - p010.1 - p100.0 + p100.1 - p101.0 - p110.1 + p111.1 + 1\\- p000.0 + p000.1 - p001.0 - p010.1 - p101.0 - p110.1 + p111.1 + 1\\p000.0 + p100.1 + p111.0 + p111.1\\p000.1 + p100.0 + p111.0 + p111.1\\- p001.0 - p010.0 - p100.0 + p100.1 - p101.0 - p110.1 + p111.1 + 1\\- p000.0 + p000.1 - p001.0 - p010.0 - p101.0 - p110.1 + p111.1 + 1\\- p001.0 - p010.1 - p100.0 + p100.1 - p101.0 - p110.0 + p111.1 + 1\\- p000.0 + p000.1 - p001.0 - p010.1 - p101.0 - p110.0 + p111.1 + 1
\end{matrix}\right\}

2. Sharp bounds of $\bar{\delta}(0)$ (NIE(0))

Lower bound

\max\left\{\begin{matrix}
- p011.1 - p100.1 + p110.0 - p110.1 + p111.0 - p111.1\\p000.1 + p001.1 + p010.0 + p101.1 + p110.0 + p111.0 - 1\\- p011.0 - p100.0 - p100.1 - p110.1 + p111.0 - p111.1\\p001.0 + p010.0 - p100.1 + p101.1 + p110.0 - p110.1 + 2 p111.0 - p111.1 - 1\\p001.1 + p010.0 - p100.1 + p101.0 + p110.0 - p110.1 + 2 p111.0 - p111.1 - 1\\p001.1 + p010.0 - p100.1 + p101.1 + p110.0 - p110.1 + 2 p111.0 - p111.1 - 1\\- p011.1 - p100.0 - p100.1 - p110.1\\- p000.0 - p011.1 - p100.0 - p100.1 - p101.0 + p101.1 - p110.1\\- p000.0 - p001.0 + p001.1 - p011.1 - p100.0 - p100.1 - p110.1\\p001.1 + p010.0 + p011.0 - p011.1 - p100.1 + p101.1 + p110.0 - p110.1 + p111.0 - 1\\- p011.0 - p100.0 - p100.1 - p111.1\\- p000.0 - p011.0 - p100.0 - p100.1 - p101.0 + p101.1 - p111.1\\- p000.0 - p001.0 + p001.1 - p011.0 - p100.0 - p100.1 - p111.1\\p001.1 + p010.0 - p100.1 + p101.1 + p110.0 + p111.0 - p111.1 - 1\\- p011.1 - p100.0 - p100.1 - p111.0\\- p010.0 + p010.1 - p011.0 - p100.0\\- p011.0 - p100.0\\p001.0 + p010.1 - p011.0 + p011.1 - p100.0 + p101.0 + p111.0 - 1\\p001.0 + p010.1 - p011.0 + p011.1 - p100.0 + p101.0 + p110.1 - 1\\- p000.1 + p001.0 - p001.1 - p011.1 - p100.0 - p100.1 + p101.0 - p101.1 - p110.1\\- p000.1 + p001.0 - p001.1 - p011.1 - p100.0 - p100.1 + p101.0 - p101.1 - p111.0\\p001.0 + p010.0 + p011.0 - p011.1 - p100.1 + p101.1 + p110.0 - 1\\- p000.1 + 2 p001.0 - p001.1 + p010.0 + p011.0 - p011.1 - p100.1 + p101.1 + p110.0 - 1\\- p000.0 - p000.1 + p001.0 - p001.1 - p011.1 - p100.0 - p100.1 - p101.0 + p101.1 - p110.1\\p001.0 + p010.1 + p101.1 + p110.0 + p111.0 - 1\\p001.0 + p010.1 - p011.0 + p011.1 - p100.0 + p101.1 + p111.0 - 1\\2 p001.0 + p010.0 + p010.1 + p011.1 + 2 p101.1 + p110.0 + 2 p111.0 - 2\\- p000.1 + p001.0 - p001.1 - p011.0 - p100.0 - p100.1 - p111.1\\2 p001.0 + p010.0 + p010.1 + p011.1 + 2 p101.1 + p110.0 + p110.1 + p111.0 - 2\\- p000.1 + p001.0 - p001.1 - p011.1 - p100.0 - p100.1 - p110.1\\- p000.1 + p001.0 - p001.1 - p011.1 - p100.0 - p100.1 - p111.0\\p001.0 + p010.0 + p101.1 + p110.0 + p111.0 - 1\\p001.1 + p010.0 + p011.0 - p011.1 - p100.1 + p101.0 + p110.0 - 1\\p001.1 + p010.0 + p011.0 - p011.1 - p100.1 + p101.1 + p110.0 - 1\\p001.1 + p010.1 + p101.0 + p110.0 + p111.0 - 1\\2 p001.1 + p010.0 + p010.1 + p011.1 + 2 p101.0 + p110.0 + 2 p111.0 - 2\\p001.1 + p010.1 - p011.0 + p011.1 - p100.0 + p101.0 + p111.0 - 1\\2 p001.1 + p010.0 + p010.1 + p011.1 + 2 p101.0 + p110.0 + p110.1 + p111.0 - 2\\- p000.1 - p011.0 - p100.0 - p100.1 + p101.0 - p101.1 - p111.1\\- p000.0 - p000.1 - p001.0 + p001.1 - p011.1 - p100.0 - p100.1 + p101.0 - p101.1 - p110.1\\- p000.1 - p011.1 - p100.0 - p100.1 + p101.0 - p101.1 - p110.1\\- p000.1 + p001.1 + p010.0 + p011.0 - p011.1 - p100.1 + 2 p101.0 - p101.1 + p110.0 - 1\\- p000.1 - p011.1 - p100.0 - p100.1 + p101.0 - p101.1 - p111.0\\p001.1 + p010.0 + p101.0 + p110.0 + p111.0 - 1
\end{matrix}\right\}

Upper bound

\min\left\{\begin{matrix}
p000.0 + p000.1 + p001.0 - p001.1 + p010.1 + p100.0 + p111.1\\p000.0 + p001.0 - 2 p001.1 - p011.1 + p100.0 - p100.1 + p101.0 - 2 p101.1 - p110.1 + 1\\p000.0 + p000.1 + p010.1 + p100.0 + p101.0 - p101.1 + p111.1\\p000.0 + p000.1 + p010.1 + p111.1\\- 2 p001.1 - p010.0 - p010.1 - p011.1 - 2 p101.0 - p110.0 - p110.1 - p111.0 + 2\\p000.0 + p000.1 + p011.0 + p100.1 - p101.0 + p101.1 + p111.1\\p000.0 + p000.1 + p001.0 - p001.1 + p011.0 + p100.0 + p111.1\\p000.0 - p001.0 - p010.1 + p011.0 - p011.1 - p101.0 - p110.1 + 1\\p000.1 - p001.1 - p010.0 - p101.1 - p110.0 - p111.0 + p111.1 + 1\\- 2 p001.0 - p010.0 - p010.1 - p011.1 - 2 p101.1 - p110.0 - p110.1 - p111.0 + 2\\p000.0 + p000.1 - p001.0 + p001.1 + p011.0 + p100.1 + p111.1\\p000.0 + p000.1 + p011.0 + p100.0 + p101.0 - p101.1 + p111.1\\p000.0 + p000.1 + p011.0 + p111.1\\p000.0 + p001.0 - 2 p001.1 - p011.1 + p100.0 - p101.0 - p110.1 + 1\\p000.0 - p001.1 - p011.1 - p101.0 - p110.1 + 1\\p000.0 - p001.0 - p011.1 - p101.0 - p110.1 + 1\\p000.0 - p001.0 - p011.1 + p100.0 + p101.0 - 2 p101.1 - p110.1 + 1\\p000.0 - p001.0 - p011.1 - p101.1 - p110.1 + 1\\- p001.1 - p010.0 - p011.0 - p101.0 - p110.1 + 1\\- p001.0 - p010.0 - p011.0 - p101.1 - p110.1 + 1\\p000.0 + p110.0 - p110.1 + p111.0\\p000.1 - p001.1 - p010.0 - p011.0 + p011.1 + p100.1 - 2 p101.0 + p101.1 - p110.0 + 1\\p000.1 - p001.1 - p010.0 - p011.0 + p011.1 - p101.0 - p110.0 + 1\\- 2 p001.1 - p010.0 - 2 p011.0 - 2 p101.0 - p110.0 - p110.1 - p111.1 + 2\\p000.1 - 2 p001.0 + p001.1 - p010.0 - p011.0 + p011.1 + p100.1 - p101.1 - p110.0 + 1\\p000.1 - p001.0 - p010.0 - p011.0 + p011.1 - p101.1 - p110.0 + 1\\- 2 p001.0 - p010.0 - 2 p011.0 - 2 p101.1 - p110.0 - p110.1 - p111.1 + 2\\p000.1 - p001.1 - p010.0 - p011.0 + p011.1 - p101.1 - p110.0 + 1\\p000.0 + p000.1 - p001.0 + p001.1 + p011.1 + p100.1 - p101.0 + p101.1 + p111.0\\p000.0 - p001.0 - p011.0 - p101.0 - p110.1 + p111.0 - p111.1 + 1\\p000.0 + p000.1 + p011.1 + p100.1 - p101.0 + p101.1 + p111.0\\p000.0 - p001.1 - p011.0 - p101.0 - p110.1 + p111.0 - p111.1 + 1\\p000.0 + p000.1 - p001.0 + p001.1 + p011.1 + p100.1 + p111.0\\p000.0 - p001.0 - p011.0 - p101.1 - p110.1 + p111.0 - p111.1 + 1\\p000.0 + p001.0 - p001.1 + p100.0 + p111.0\\p000.0 + p100.0 + p101.0 - p101.1 + p111.0\\p000.0 + p000.1 + p011.1 + p111.0\\p000.0 + p111.0\\p000.0 + p000.1 + p010.1 - p011.0 + p011.1 + p111.0\\p000.1 - p001.1 - p010.0 + p010.1 - 2 p011.0 + p011.1 - p101.1 - p110.0 + 1\\p000.1 - p001.0 - p010.0 + p010.1 - 2 p011.0 + p011.1 - p101.1 - p110.0 + 1\\p000.1 - p001.1 - p010.0 + p010.1 - 2 p011.0 + p011.1 - p101.0 - p110.0 + 1\\- p001.1 - p010.0 - p011.0 - p100.1 - p101.1 - p110.0 + 1\\- p001.1 - p010.0 - p011.0 - p100.1 - p101.1 - p110.1 + 1
\end{matrix}\right\}

3. Sharp bounds of $\bar{\xi}(1)$ (NDE(1))

Lower bound

\max\left\{\begin{matrix}
- p000.0 + p000.1 + p010.1 + p101.0 - p110.0 + p110.1 + p111.1 - 1\\- p000.0 + p000.1 + p010.1 + p101.0 + p111.1 - 1\\- p000.0 - p001.1 - p100.0 - p100.1 + p101.0 - p101.1 - p110.0\\- p000.0 + p000.1 + p010.0 + p101.0 - p110.0 + p110.1 + p111.1 - 1\\- p000.0 + p000.1 + p010.0 + p101.0 + p111.1 - 1\\- p000.0 + p000.1 - p001.1 + p010.1 - p011.1 + p100.0 - p100.1 + p101.0 - p110.0 + p110.1 - 1\\- p000.0 + 2 p000.1 + 2 p010.1 + p100.0 + p101.0 + p101.1 + p110.0 + p111.1 - 2\\- p000.0 - 2 p001.0 + p001.1 - 2 p100.0 - p100.1 + p101.0 - p101.1 - p110.0\\- p000.0 + p000.1 - 2 p001.0 + 2 p001.1 + p010.1 - 2 p100.0 + p101.0 + p111.1 - 1\\- p000.0 - p001.0 - p100.0 - p100.1 + p101.0 - p101.1 - p110.0\\- p000.0 + p000.1 - 2 p001.0 + 2 p001.1 + p010.0 - 2 p100.0 + p101.0 + p111.1 - 1\\- 2 p000.0 + p000.1 - 3 p001.0 + 2 p001.1 - p011.0 - 3 p100.0 - 2 p110.0 + p110.1 - p111.0 + p111.1\\- p000.0 + 2 p000.1 + 2 p010.0 + p100.0 + p101.0 + p101.1 - p110.0 + 2 p110.1 + p111.1 - 2\\- 2 p000.0 + 2 p000.1 - p001.0 + p010.0 - p011.0 + p101.1 - p111.0 + p111.1 - 1\\- p000.0 - 2 p001.0 + p001.1 - 2 p100.0 - 2 p101.0 + 2 p101.1 - p110.0\\- p000.0 - 2 p001.0 + p001.1 - p011.1 - 2 p100.0 - 2 p101.0 + 2 p101.1 - p110.1\\- p000.0 - p001.0 - 2 p100.0 - 2 p101.0 + 2 p101.1 - p110.0\\- p000.0 - p001.0 - p011.1 - 2 p100.0 - 2 p101.0 + 2 p101.1 - p110.1\\- p000.0 - 2 p001.0 + p001.1 - 2 p100.0 - p110.0\\- p000.0 - 2 p001.0 + p001.1 - p011.1 - 2 p100.0 - p110.1\\- p000.0 - p001.0 - p100.0 - p110.0\\- p000.0 - p001.0 - p100.0 - p101.0 + p101.1 - p110.0\\- p000.0 - p001.0 - p011.1 - p100.0 - p110.1\\- p000.0 - p001.0 - p011.1 - p100.0 - p101.0 + p101.1 - p110.1\\- p000.0 + p000.1 + p010.1 - 2 p100.0 - 2 p101.0 + 3 p101.1 + p111.1 - 1\\- p000.0 - p001.1 - 2 p100.0 - p100.1 - 2 p101.0 + 2 p101.1 - p110.0\\- p000.0 - p001.1 - p011.1 - p100.1 - p110.0\\- p000.0 + p000.1 + p010.1 + p101.1 + p111.1 - 1\\- p000.0 - p001.1 - p100.0 - p100.1 - p101.0 + p101.1 - p110.0\\- p000.0 + p000.1 - 2 p001.0 + 2 p001.1 + p010.0 - 2 p100.0 + p100.1 - 2 p101.0 + 3 p101.1 + p111.1 - 1\\- p000.0 - 2 p001.0 + p001.1 + p010.0 - p010.1 - p011.1 - 2 p100.0 - 2 p101.0 + 2 p101.1 - p110.0\\- p000.0 - p001.0 + p010.0 - p010.1 - p011.1 - 2 p100.0 - 2 p101.0 + 2 p101.1 - p110.1\\- p000.0 - p001.0 + p010.0 - p010.1 - p011.1 - 2 p100.0 - 2 p101.0 + 2 p101.1 - p110.0\\- p000.0 - 2 p001.0 + p001.1 + p010.0 - p010.1 - p011.1 - 2 p100.0 - p110.1\\- p000.0 - p001.0 + p010.0 - p010.1 - p011.1 - p100.0 - p110.1\\- p000.0 - p001.0 + p010.0 - p010.1 - p011.1 - p100.0 - p101.0 + p101.1 - p110.1\\- p000.0 - 2 p001.0 + p001.1 + p010.0 - p010.1 - p011.1 - 2 p100.0 - p110.0\\- p000.0 - p001.0 + p010.0 - p010.1 - p011.1 - p100.0 - p110.0\\- p000.0 - p001.0 + p010.0 - p010.1 - p011.1 - p100.0 - p101.0 + p101.1 - p110.0\\- p000.0 + p000.1 + p010.0 - 2 p100.0 - 2 p101.0 + 3 p101.1 - p110.0 + p110.1 + p111.1 - 1\\- p000.0 + p000.1 + p010.0 - 2 p100.0 - 2 p101.0 + 3 p101.1 + p111.1 - 1\\- p000.0 + p000.1 + p010.0 + p101.1 - p110.0 + p110.1 + p111.1 - 1\\- p000.0 + p000.1 + p010.0 + p101.1 + p111.1 - 1\\p001.0 - p001.1 + p010.1 - p100.1 + 2 p101.0 - p101.1 - p110.0 + p110.1 + p111.1 - 1\\p001.0 - p001.1 + p010.1 - p100.1 + 2 p101.0 - p101.1 + p111.1 - 1\\p001.0 - p001.1 + p010.0 + p011.0 - p100.1 + 2 p101.0 - p101.1 + p111.1 - 1\\p001.0 - p001.1 + p010.0 - p100.1 + 2 p101.0 - p101.1 - p110.0 + p110.1 + p111.1 - 1\\- p000.1 - p001.0 - p011.1 - p100.0 - 2 p100.1 + 2 p101.0 - 2 p101.1 - p110.0\\- p001.0 + p001.1 + p010.1 - p100.0 - p100.1 + 2 p101.0 - p101.1 + p111.1 - 1\\p010.1 - p100.1 + 2 p101.0 - p101.1 - p110.0 + p110.1 + p111.1 - 1\\p010.1 - p100.1 + 2 p101.0 - p101.1 + p111.1 - 1\\- p001.0 + p001.1 + p010.0 + p011.0 - p100.0 - p100.1 + 2 p101.0 - p101.1 + p111.1 - 1\\p010.0 + p011.0 - p100.1 + 2 p101.0 - p101.1 + p111.1 - 1\\- p001.0 + p001.1 + p010.0 - p100.0 - p100.1 + 2 p101.0 - p101.1 - p110.0 + p110.1 + p111.1 - 1\\p010.0 - p100.1 + 2 p101.0 - p101.1 - p110.0 + p110.1 + p111.1 - 1\\- p000.1 - p001.0 - p011.1 - p100.0 - p101.0 + p101.1 - p110.0\\- p000.1 - p001.0 - p011.1 - p100.0 - p101.0 + p101.1 - p110.1\\p000.0 - 2 p000.1 - p001.0 - p001.1 - 2 p011.1 - p100.0 - p110.0 - p111.1\\p000.0 - p000.1 - p001.0 + p010.1 - p011.1 - p100.0 + p100.1 + p101.1 + p110.0 - p110.1 - 1\\- p000.1 - p001.0 - p011.1 - p100.0 - p110.0\\- p000.1 - p001.0 - p011.1 - p100.0 - p110.1\\- p000.1 + p001.0 - 2 p001.1 - p011.1 - p100.0 - 2 p100.1 - p101.0 + p101.1 - p110.0\\- p000.1 + p001.0 - 2 p001.1 - p011.1 - 2 p100.1 - p110.0\\p010.1 + p101.0 - p110.0 + p110.1 + p111.1 - 1\\p010.1 + p101.1 - p110.0 + p110.1 + p111.1 - 1\\p001.0 - p001.1 + p010.1 - p100.0 - p100.1 - p101.0 + 2 p101.1 + p111.1 - 1\\p001.0 - p001.1 + p010.1 - p100.1 + p101.1 + p111.1 - 1\\p010.1 + p101.0 + p111.1 - 1\\p010.1 + p101.1 + p111.1 - 1\\- p000.1 - p001.0 + p010.0 - p010.1 - p011.1 - p100.0 - p101.0 + p101.1 - p110.0\\- p001.0 + p001.1 + p010.0 - p100.0 + p100.1 - p101.0 + 2 p101.1 + p111.1 - 1\\p000.0 - p000.1 - p001.0 + 2 p010.0 - p010.1 - p011.1 - p100.0 + p100.1 + p101.1 - p110.0 + p110.1 - 1\\p000.0 - p001.0 + p001.1 + 2 p010.0 - p100.0 + 2 p100.1 + 2 p101.1 + p110.0 + p111.1 - 2\\- p000.1 - p001.0 + p010.0 - p010.1 - p011.1 - p100.0 - p110.0\\- p001.0 + p001.1 + p010.0 - p100.0 + p100.1 + p101.1 + p111.1 - 1\\- p001.0 + p001.1 + p010.0 + p011.0 - p100.0 - p101.0 + 2 p101.1 + p111.1 - 1\\- p000.0 - p001.1 - 2 p100.0 - p100.1 - 2 p101.0 + 2 p101.1 - p110.0 - p111.0 + p111.1\\p010.0 + p011.0 - p100.0 - p101.0 + 2 p101.1 + p111.1 - 1\\p001.0 - p001.1 + p010.0 - p100.0 - p100.1 - p101.0 + 2 p101.1 - p110.0 + p110.1 + p111.1 - 1\\p001.0 - p001.1 + p010.0 + p011.0 - p100.1 + p101.1 + p111.1 - 1\\- p000.0 - 2 p001.0 + p001.1 - 2 p100.0 - p110.0 - p111.0 + p111.1\\p010.0 + p011.0 + p101.0 + p111.1 - 1\\p010.0 + p011.0 + p101.1 + p111.1 - 1\\p001.0 - p001.1 + p010.0 - p100.1 + p101.1 - p110.0 + p110.1 + p111.1 - 1\\p010.0 + p101.0 - p110.0 + p110.1 + p111.1 - 1\\p010.0 + p101.1 - p110.0 + p110.1 + p111.1 - 1
\end{matrix}\right\}

Upper bound

\min\left\{\begin{matrix}
p000.1 - p001.0 + p001.1 + p010.1 + p100.0 + p101.1 - p110.0 + p110.1 + p111.1\\p000.1 - p001.0 + p001.1 + p010.0 + p100.0 + p101.1 - p110.0 + p110.1 + p111.1\\2 p000.0 + p000.1 - p001.0 + p001.1 + p010.1 + p100.0 + 2 p101.0 - p101.1 - p110.0 + p110.1 + p111.1\\p000.0 + p000.1 - 2 p001.0 + p001.1 - p011.0 + p101.0 - p101.1 - 2 p110.0 + p110.1 - p111.0 + p111.1 + 1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 + p010.0 + p011.1 + p100.0 + 2 p101.1 - 2 p110.0 + 2 p110.1 + 2 p111.1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 - p010.0 + 2 p010.1 + p011.1 + p100.0 + 2 p101.1 - 2 p110.0 + 2 p110.1 + 2 p111.1\\2 p000.0 + 2 p001.0 - 2 p001.1 + p010.1 + p100.0 + 2 p101.0 - p101.1 - p110.0 + p110.1 + p111.1\\2 p000.0 + 2 p001.0 - 2 p001.1 + p010.1 + p100.0 + p101.0 - p110.0 + p110.1 + p111.1\\2 p000.0 + p000.1 + 2 p001.0 - 2 p001.1 + p010.1 + p100.0 + p101.1 - p110.0 + p110.1 + p111.1\\p000.0 + p010.1 + p100.0 + p101.0 - p110.0 + p110.1 + p111.1\\- p001.1 - p010.0 + p010.1 - p011.0 - 2 p110.0 + p110.1 - p111.0 + p111.1 + 1\\2 p000.0 + p010.1 + p100.0 + 2 p101.0 - p101.1 - p110.0 + p110.1 + p111.1\\p000.1 + p010.1 + p100.0 + p101.1 - p110.0 + p110.1 + p111.1\\p000.1 + p010.0 + p100.0 + p101.1 - p110.0 + p110.1 + p111.1\\p000.0 + p001.0 - 2 p001.1 - p011.0 + p101.0 - p101.1 - 2 p110.0 + p110.1 - p111.0 + p111.1 + 1\\p000.0 + p001.0 - 2 p001.1 - p011.0 - 2 p110.0 + p110.1 - p111.0 + p111.1 + 1\\2 p000.0 + p000.1 + 2 p001.0 - 2 p001.1 + p010.0 + p100.0 + p101.1 - p110.0 + p110.1 + p111.1\\- p001.0 - p011.0 - 2 p110.0 + p110.1 - p111.0 + p111.1 + 1\\- p001.1 - p011.0 - 2 p110.0 + p110.1 - p111.0 + p111.1 + 1\\2 p000.0 + p010.0 + p100.0 + 2 p101.0 - p101.1 - p110.0 + p110.1 + p111.1\\p000.1 - 2 p001.0 + p001.1 - p011.1 - p101.0 + p101.1 - p110.0 - p111.0 + 1\\2 p000.1 - 2 p001.0 + 2 p001.1 + p010.0 + p100.1 - p101.0 + 2 p101.1 - p110.0 + p110.1 + p111.1\\2 p000.1 - 3 p001.0 + 2 p001.1 - p011.0 - p100.0 + p100.1 - 2 p110.0 + p110.1 - p111.0 + p111.1 + 1\\p000.1 - 2 p001.0 + p001.1 - p011.1 - p110.0 - p111.0 + 1\\p000.0 + p000.1 - 2 p001.0 + p001.1 - p011.1 + p101.0 - p101.1 - p110.0 - p111.0 + 1\\2 p000.1 - 2 p001.0 + 2 p001.1 + p010.0 + p100.1 + p101.1 - p110.0 + p110.1 + p111.1\\- p001.1 - p011.0 - p100.0 + p100.1 - 2 p110.0 + p110.1 - p111.0 + p111.1 + 1\\p000.0 + p001.0 - p001.1 + p010.1 + p100.1 + p101.0 - p110.0 + p110.1 + p111.1\\p000.0 + p001.0 - 2 p001.1 - p011.1 + p101.0 - p101.1 - p110.0 - p111.0 + 1\\p000.0 + p001.0 - 2 p001.1 - p011.1 - p110.0 - p111.0 + 1\\p000.0 + p000.1 + p001.0 - 2 p001.1 - p011.1 - p101.0 + p101.1 - p110.0 - p111.0 + 1\\p000.0 + p010.0 + p100.1 + p101.0 - p110.0 + p110.1 + p111.1\\p000.0 + p010.1 + p100.1 + p101.0 - p110.0 + p110.1 + p111.1\\p000.1 - p001.1 - p011.1 - p101.0 + p101.1 - p110.0 - p111.0 + 1\\- p001.0 - p011.1 - p110.0 - p111.0 + 1\\- p001.1 - p011.1 - p110.0 - p111.0 + 1\\p000.0 - p001.0 - p011.1 + p101.0 - p101.1 - p110.0 - p111.0 + 1\\2 p000.1 - p001.1 - p011.0 - p100.0 + p100.1 - 2 p101.0 + 2 p101.1 - 2 p110.0 + p110.1 - p111.0 + p111.1 + 1\\p000.1 - p001.0 + p001.1 + p010.0 + p100.1 + p101.1 - p110.0 + p110.1 + p111.1\\p000.1 + p010.0 + p100.1 + p101.1 - p110.0 + p110.1 + p111.1\\2 p000.1 + p010.0 + p100.1 - p101.0 + 2 p101.1 - p110.0 + p110.1 + p111.1\\p000.0 - p010.0 + 2 p010.1 + p011.1 - p100.0 + 2 p100.1 + p101.0 + p101.1 - 2 p110.0 + 2 p110.1 + 2 p111.1\\- p001.0 - p011.0 + p011.1 - 2 p100.0 + 2 p100.1 + p101.1 - 3 p110.0 + 2 p110.1 - p111.0 + 2 p111.1 + 1\\p000.1 + p010.1 + p100.1 + p101.1 + p111.1\\p000.1 - p001.0 + p001.1 + p010.1 + p100.1 + p101.1 + p111.1\\2 p000.1 + p010.1 + p100.1 - p101.0 + 2 p101.1 + p111.1\\p000.0 + 2 p000.1 + p001.0 - p001.1 + p010.1 + p100.1 - p101.0 + 2 p101.1 + p111.1\\p000.0 + 2 p000.1 - 2 p001.0 + 2 p001.1 + p010.1 + p100.1 + p101.0 + p111.1\\2 p000.1 - 2 p001.0 + 2 p001.1 + p010.1 + p100.1 + p101.1 + p111.1\\2 p000.1 - 2 p001.0 + 2 p001.1 + p010.1 + p100.1 - p101.0 + 2 p101.1 + p111.1\\p000.0 + p010.0 + p011.1 - p100.0 + 2 p100.1 + p101.0 + p101.1 + 2 p111.1\\p000.0 - p010.0 + 2 p010.1 + p011.1 - p100.0 + 2 p100.1 + p101.0 + p101.1 + 2 p111.1\\2 p000.1 + p010.0 + p100.1 - p101.0 + 2 p101.1 + p111.1\\p000.1 - p001.0 + p001.1 + p010.0 + p100.1 + p101.1 + p111.1\\p000.1 + p010.0 + p100.1 + p101.1 + p111.1\\p000.0 + 2 p000.1 + p001.0 - p001.1 + p010.0 + p100.1 - p101.0 + 2 p101.1 + p111.1\\p000.0 + p010.1 + p100.1 + p101.0 + p111.1\\p000.0 + p010.0 + p100.1 + p101.0 + p111.1\\p000.0 + p001.0 - p001.1 + p010.1 + p100.1 + p101.0 + p111.1\\- p001.1 - p011.0 - p100.0 + p100.1 - p110.0 - p111.0 + p111.1 + 1\\2 p000.1 - 2 p001.0 + 2 p001.1 + p010.0 + p100.1 + p101.1 + p111.1\\p000.0 + 2 p000.1 - 2 p001.0 + 2 p001.1 + p010.0 + p100.1 + p101.0 + p111.1\\2 p000.1 - 2 p001.0 + 2 p001.1 + p010.0 + p100.1 - p101.0 + 2 p101.1 + p111.1\\p000.1 - p001.1 - p011.0 - p101.0 + p101.1 - p110.0 - p111.0 + 1\\p000.1 + p010.0 + p100.0 + p101.1 + p111.1\\p000.1 + p010.1 + p100.0 + p101.1 + p111.1\\2 p000.0 + p010.0 + p100.0 + 2 p101.0 - p101.1\\- p001.1 - p011.0 - p110.0 - p111.0 + 1\\- p001.0 - p011.0 - p110.0 - p111.0 + 1\\2 p000.0 + p010.1 + p100.0 + 2 p101.0 - p101.1 + p111.1\\- p001.1 - p010.0 + p010.1 - p011.0 - p110.0 - p111.0 + p111.1 + 1\\p000.0 + p010.1 + p100.0 + p101.0 + p111.1\\2 p000.0 + p000.1 + 2 p001.0 - 2 p001.1 + p010.1 + p100.0 + p101.1 + p111.1\\2 p000.0 + p000.1 + 2 p001.0 - 2 p001.1 + p010.0 + p100.0 + p101.1\\p000.0 + p001.0 - 2 p001.1 - p011.0 - p110.0 - p111.0 + 1\\2 p000.0 + 2 p001.0 - 2 p001.1 + p010.1 + p100.0 + p101.0 + p111.1\\p000.0 + p001.0 - 2 p001.1 - p011.0 + p101.0 - p101.1 - p110.0 - p111.0 + 1\\2 p000.0 + 2 p001.0 - 2 p001.1 + p010.1 + p100.0 + 2 p101.0 - p101.1 + p111.1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 - p010.0 + 2 p010.1 + p011.1 + p100.0 + 2 p101.1 + 2 p111.1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 + p010.0 + p011.1 + p100.0 + 2 p101.1 + 2 p111.1\\2 p000.0 + p000.1 - p001.0 + p001.1 + p010.0 + p100.0 + 2 p101.0 - p101.1\\p000.1 - 2 p001.0 + p001.1 - p011.0 - p110.0 - p111.0 + 1\\2 p000.0 + p000.1 - p001.0 + p001.1 + p010.1 + p100.0 + 2 p101.0 - p101.1 + p111.1\\p000.0 + p000.1 - p001.0 + p001.1 + p010.0 + p100.0 + p101.1\\p000.1 - p001.0 + p001.1 + p010.0 + p100.0 + p101.1 + p111.1\\p000.1 - p001.0 + p001.1 + p010.1 + p100.0 + p101.1 + p111.1
\end{matrix}\right\}

4. Sharp bounds of $\bar{\xi}(0)$ (NDE(0))

Lower bound

\max\left\{\begin{matrix}
p000.0 + p000.1 + p001.0 + 2 p010.1 + p011.1 + 2 p101.0 + p110.1 + p111.0 - 2\\p000.0 + p010.1 - p100.1 + 2 p101.0 - p101.1 + p111.0 - p111.1 - 1\\p000.1 - p010.0 + 2 p010.1 - p011.0 + p101.0 - p110.0 + p110.1 - 1\\p000.0 + p001.0 - p001.1 - p010.0 + 2 p010.1 - p011.0 - p100.1 + 2 p101.0 - p101.1 - p110.0 + p110.1 - 1\\p000.1 - p010.0 + 2 p010.1 - p011.0 + p101.0 - 1\\p000.1 - p010.0 + 2 p010.1 - p011.0 - p011.1 + p101.0 + p110.0 - p110.1 - 1\\p000.0 + p000.1 + p001.1 + 2 p010.1 - p011.1 + 2 p101.0 + 2 p110.0 - p110.1 + p111.0 - 2\\- p000.0 + p000.1 - p010.0 + 2 p010.1 - 2 p011.0 + 2 p011.1 - 2 p100.0 + p101.0 - 2 p110.0 + p110.1 - 1\\p000.1 + p001.0 + 2 p010.1 - p011.0 + 2 p011.1 - p100.0 + 2 p101.0 - p110.0 + 2 p110.1 - 2\\- p001.0 + p001.1 + p010.1 - p011.0 + p011.1 - p100.0 - p100.1 + 2 p101.0 - p101.1 - p110.0 + p111.0 - p111.1 - 1\\- p000.1 - p001.0 - p011.0 - p100.0 - 2 p100.1 + 2 p101.0 - 2 p101.1 - p110.0 - 2 p111.1\\- p001.1 - 2 p010.0 + 2 p010.1 - 2 p011.0 - p011.1 - p100.0 - p100.1 + p101.0 - p101.1 - p110.1 - p111.0\\p000.0 + p001.0 - p001.1 - p010.0 + 2 p010.1 - p011.0 - p100.1 + 2 p101.0 - p101.1 - 1\\- p001.1 - p011.0 - p100.0 - p100.1 + p101.0 - p101.1 - p110.0 - p111.1\\p000.0 + p010.0 - p100.1 + 2 p101.0 - p101.1 + p111.0 - p111.1 - 1\\p000.1 + p010.1 + p101.0 - 1\\p000.1 + p010.1 - p011.1 + p101.0 + p110.0 - p110.1 - 1\\p000.1 + p010.0 + p101.0 - 1\\p000.1 + p010.0 - p011.0 + p101.0 - p110.0 + p110.1 - 1\\p000.1 - p001.0 + p001.1 + p010.1 - p100.0 + p101.0 - 1\\- p001.0 - 2 p011.1 - p100.0 - p100.1 + p101.0 - p101.1 + p110.0 - 2 p110.1 - p111.1\\p000.1 - p001.0 + p001.1 + p010.0 - p100.0 + p101.0 - 1\\- p001.1 - 2 p011.0 - p100.0 - p100.1 + p101.0 - p101.1 - 2 p110.0 + p110.1 - p111.0\\p000.0 + p001.0 - p001.1 + p010.0 - p100.1 + 2 p101.0 - p101.1 - 1\\p000.0 + p001.0 - p001.1 + p010.1 - p100.1 + 2 p101.0 - p101.1 - 1\\- p001.0 - p011.1 - p100.0 - p100.1 + p101.0 - p101.1 - p110.1 - p111.0\\- p001.1 - p011.1 - p100.0 - p100.1 + p101.0 - p101.1 - p110.1 - p111.0\\p000.0 - p000.1 + 2 p010.0 - p010.1 + 2 p011.0 - 2 p011.1 - 2 p100.1 + 3 p101.0 - 2 p101.1 + p110.0 - p110.1 - p111.0 - 1\\p000.0 - p000.1 + 2 p010.0 - p010.1 + 2 p011.0 - 2 p011.1 - 2 p100.1 + 3 p101.0 - 2 p101.1 + p110.0 - 2 p110.1 - 1\\- p000.1 + p001.0 - 2 p001.1 + p010.0 - p010.1 + p011.0 - 2 p011.1 - p100.0 - 2 p100.1 + 2 p101.0 - 2 p101.1 - p110.1 - 2 p111.0\\p000.0 - p000.1 + 2 p001.0 - 2 p001.1 + 2 p010.0 - p010.1 + 2 p011.0 - 2 p011.1 - 2 p100.1 + 3 p101.0 - 2 p101.1 + p110.0 - 2 p110.1 - 1\\p000.0 + p001.0 - p001.1 + 2 p010.0 - p010.1 - p011.0 - p011.1 - p100.1 + 2 p101.0 - p101.1 - p110.0 + p110.1 - 1\\p000.1 - p001.0 + p001.1 + 2 p010.0 - p010.1 - p011.1 - p100.0 + p101.0 - 1\\p000.1 + 2 p010.0 - p010.1 - p011.0 - p011.1 + p101.0 - p110.0 + p110.1 - 1\\p000.1 + 2 p010.0 - p010.1 - p011.1 + p101.0 - 1\\p000.0 + 3 p010.0 - 2 p010.1 - 2 p011.1 - p100.1 + 2 p101.0 - p101.1 + p111.0 - p111.1 - 1\\p000.1 + 2 p010.0 - p010.1 - p011.1 + p101.0 + p110.0 - p110.1 - 1\\p000.1 - p001.0 + p001.1 + 2 p010.0 - p010.1 - p011.1 - p100.0 + p101.0 + p110.0 - p110.1 - 1\\p000.0 + 2 p010.0 - p010.1 + p011.0 - p011.1 - p100.1 + 2 p101.0 - p101.1 + p110.0 - p110.1 - 1\\- p001.1 + p010.0 - p010.1 - p011.1 - p100.0 - p100.1 + p101.0 - p101.1 - p110.1 - p111.0\\p000.0 - p010.0 + 2 p010.1 - p011.0 - p100.1 + 2 p101.0 - p101.1 - p110.0 + p110.1 - 1\\p000.0 - p010.0 + 2 p010.1 - p011.0 - p100.1 + 2 p101.0 - p101.1 - 1\\p000.0 - p010.0 + 2 p010.1 - p011.0 - p011.1 - p100.1 + 2 p101.0 - p101.1 + p110.0 - p110.1 - 1\\- 2 p001.1 - p010.0 + p010.1 - p011.0 - 2 p011.1 + p100.0 - 2 p100.1 + p101.0 - p101.1 - p110.0 - 2 p111.1\\- 2 p001.1 - p010.0 + p010.1 - p011.0 - 2 p011.1 + p100.0 - 2 p100.1 + p101.0 - p101.1 + p110.0 - 2 p110.1 - 2 p111.1\\- 2 p001.1 - p010.0 + p010.1 - p011.0 - 3 p011.1 + p100.0 - 2 p100.1 + p101.0 - p101.1 + 2 p110.0 - 3 p110.1 - 2 p111.1\\p000.0 + 2 p010.0 - p010.1 - p011.0 - p011.1 - p100.1 + 2 p101.0 - p101.1 - p110.0 + p110.1 - 1\\- 2 p001.1 + 3 p010.0 - 3 p010.1 - 3 p011.1 + p100.0 - 2 p100.1 + p101.0 - p101.1 + 2 p110.0 - 3 p110.1 - 2 p111.1\\p000.1 - p001.1 + 3 p010.0 - 2 p010.1 - 2 p011.1 + p100.0 - p100.1 + p101.0 - p111.1 - 1\\- 2 p001.1 + 3 p010.0 - 3 p010.1 - p011.0 - 3 p011.1 + p100.0 - 2 p100.1 + p101.0 - p101.1 - p110.0 - 2 p111.1\\- 2 p001.1 - 2 p011.1 + p100.0 - 2 p100.1 + p101.0 - p101.1 - p110.1 - 2 p111.1\\p000.1 - p001.1 + 2 p010.0 - p010.1 - p011.1 + p100.0 - p100.1 + p101.0 - p111.1 - 1\\- 2 p001.1 + 2 p010.0 - 2 p010.1 - p011.0 - 2 p011.1 + p100.0 - 2 p100.1 + p101.0 - p101.1 - p110.0 - 2 p111.1\\- 2 p001.1 - 2 p011.1 + p100.0 - 2 p100.1 + p101.0 - p101.1 + p110.0 - 2 p110.1 - 2 p111.1\\- 2 p001.1 - 3 p011.1 + p100.0 - 2 p100.1 + p101.0 - p101.1 + 2 p110.0 - 3 p110.1 - 2 p111.1\\- 2 p001.1 + 2 p010.0 - 2 p010.1 - 2 p011.1 + p100.0 - 2 p100.1 + p101.0 - p101.1 + p110.0 - 2 p110.1 - 2 p111.1\\p000.0 + p010.0 - p011.0 - p100.1 + 2 p101.0 - p101.1 - p110.0 + p110.1 - 1\\p000.0 + p010.1 - p100.1 + 2 p101.0 - p101.1 - 1\\p000.0 + p010.0 - p100.1 + 2 p101.0 - p101.1 - 1\\p000.0 + p001.0 - p001.1 + p010.1 - p100.1 + p101.1 + p111.0 - p111.1 - 1\\p000.0 + p010.1 - p100.1 + p101.1 + p111.0 - p111.1 - 1\\p000.0 - p010.0 + 2 p010.1 - p011.0 + p101.1 - p110.0 + p110.1 - 1\\p000.0 + p001.0 - p001.1 - p010.0 + 2 p010.1 - p011.0 - p100.1 + p101.1 - p110.0 + p110.1 - 1\\2 p000.0 - p000.1 - p001.1 - p010.0 + 2 p010.1 - p011.0 - p011.1 + p101.0 - p110.0 + p110.1 - p111.1 - 1\\p000.1 - p010.0 + 2 p010.1 - p011.0 + p101.1 - p110.0 + p110.1 - 1\\p000.0 - p010.0 + 2 p010.1 - p011.0 + p101.0 - p110.0 + p110.1 - 1\\p000.0 + p010.1 - 2 p011.1 - p100.1 + p101.1 + 2 p110.0 - 2 p110.1 + p111.0 - p111.1 - 1\\p000.0 - p010.0 + 2 p010.1 - p011.0 - p011.1 + p101.1 + p110.0 - p110.1 - 1\\p000.0 - p010.0 + 2 p010.1 - p011.0 + p101.1 - 1\\p000.0 + p001.0 - p001.1 - p010.0 + 2 p010.1 - p011.0 - p100.1 + p101.1 - 1\\p000.0 + p001.0 - p001.1 - p010.0 + 2 p010.1 - p011.0 - p011.1 - p100.1 + p101.1 + p110.0 - p110.1 - 1\\p000.0 + p000.1 + p001.0 + 2 p010.1 - p011.1 + 2 p101.1 + 2 p110.0 - p110.1 + p111.0 - 2\\2 p000.0 - p000.1 - p001.1 - p010.0 + 2 p010.1 - p011.0 - p011.1 + p101.0 + p110.0 - p110.1 - p111.1 - 1\\2 p000.0 - p000.1 - p001.1 - p010.0 + 2 p010.1 - p011.0 - 2 p011.1 + p101.0 + 2 p110.0 - 2 p110.1 - p111.1 - 1\\- p000.0 - p001.1 - p010.0 + p010.1 - 2 p011.0 + p011.1 - 2 p100.0 - p100.1 - 2 p101.0 + 2 p101.1 - 2 p110.0 - p111.1\\- p000.1 - p001.0 - p011.0 - p100.0 - 2 p100.1 - p101.0 + p101.1 - p110.0 - p110.1 + p111.0 - 2 p111.1\\- p000.1 - p001.0 - p011.0 - p100.0 - 2 p100.1 - p101.0 + p101.1 - p110.0 - 2 p111.1\\- p000.1 + p001.0 - 2 p001.1 - p011.0 - p100.0 - 2 p100.1 - p101.0 + p101.1 - p110.0 - 2 p111.1\\p000.1 - p010.0 + 2 p010.1 - p011.0 + p101.1 - 1\\p000.1 - p010.0 + 2 p010.1 - p011.0 - p011.1 + p101.1 + p110.0 - p110.1 - 1\\p000.0 - p010.0 + 2 p010.1 - p011.0 + p101.0 - 1\\p000.0 - p010.0 + 2 p010.1 - p011.0 - p011.1 + p101.0 + p110.0 - p110.1 - 1\\- p001.1 - p011.0 - p100.0 - p100.1 - p101.0 + p101.1 - p110.0 - p111.1\\p000.0 + p010.0 - p100.1 + p101.1 + p111.0 - p111.1 - 1\\p000.1 - p001.0 + p001.1 + p010.1 - p100.0 - p101.0 + 2 p101.1 - 1\\- p001.0 - 2 p011.1 - p100.0 - p100.1 - p101.0 + p101.1 + p110.0 - 2 p110.1 - p111.1\\p000.1 - p001.0 + p001.1 + p010.0 - p100.0 - p101.0 + 2 p101.1 - 1\\p000.0 + p010.0 + p101.1 - 1\\p000.0 + p010.1 - p011.1 + p101.1 + p110.0 - p110.1 - 1\\p000.0 + p010.1 + p101.1 - 1\\p000.0 + p010.0 - p011.0 + p101.1 - p110.0 + p110.1 - 1\\p000.0 + p001.0 - p001.1 + p010.0 - p011.0 - p100.1 + p101.1 - p110.0 + p110.1 - 1\\p000.0 + p001.0 - p001.1 + p010.0 - p100.1 + p101.1 - 1\\p000.0 + p001.0 - p001.1 + p010.1 - p100.1 + p101.1 - 1\\p000.0 + p010.0 + p011.0 - p011.1 - p100.1 + p101.1 + p110.0 - p110.1 - 1\\- p001.1 - p011.1 - p100.0 - p100.1 - p101.0 + p101.1 - p110.1 - p111.0\\p000.0 - p000.1 + 2 p010.0 - p010.1 + 2 p011.0 - 2 p011.1 - 2 p100.1 + p101.1 + p110.0 - p110.1 - p111.0 - 1\\p000.0 - p000.1 + 2 p010.0 - p010.1 + 2 p011.0 - 2 p011.1 - 2 p100.1 + p101.1 + p110.0 - 2 p110.1 - 1\\p000.0 - 2 p000.1 + 2 p001.0 - 3 p001.1 + 2 p010.0 - 2 p010.1 + 2 p011.0 - 3 p011.1 - 3 p100.1 + p110.0 - 2 p110.1 - p111.0 - p111.1\\p000.0 - 2 p000.1 + 2 p001.0 - 3 p001.1 + 2 p010.0 - 2 p010.1 + 2 p011.0 - 3 p011.1 - 3 p100.1 + p110.0 - 3 p110.1 - p111.1\\p000.0 + 2 p010.0 - p010.1 - p011.1 + p101.1 - 1\\p000.0 + 2 p010.0 - p010.1 - p011.0 - p011.1 + p101.1 - p110.0 + p110.1 - 1\\p000.0 - p000.1 + p001.0 - 2 p001.1 + 2 p010.0 - 2 p010.1 - p011.0 - 2 p011.1 - 2 p100.1 - p110.0 - p111.1\\p000.1 - p001.0 + p001.1 + 2 p010.0 - p010.1 - p011.1 - p100.0 - p101.0 + 2 p101.1 - 1\\p000.0 + 3 p010.0 - 2 p010.1 - 2 p011.1 - p100.1 + p101.1 + p111.0 - p111.1 - 1\\- p001.0 + 2 p010.0 - 2 p010.1 - 2 p011.1 - p100.0 - p100.1 - p101.0 + p101.1 + p110.0 - 2 p110.1 - p111.1\\p000.0 + 2 p010.0 - p010.1 - p011.1 + p101.1 + p110.0 - p110.1 - 1\\p000.0 + 2 p010.0 - p010.1 + p011.0 - p011.1 - p100.1 + p101.1 + p110.0 - p110.1 - 1\\- p001.1 + p010.0 - p010.1 - p011.1 - p100.0 - p100.1 - p101.0 + p101.1 - p110.1 - p111.0\\p000.1 + 2 p010.0 - p010.1 - p011.1 - p100.0 - p101.0 + 2 p101.1 + p110.0 - p110.1 - 1\\p000.1 + 2 p010.0 - p010.1 - p011.1 - p100.0 - p101.0 + 2 p101.1 - 1\\p000.0 + p000.1 + p001.0 + 3 p010.0 - p010.1 - p011.1 + 2 p101.1 + p110.1 + p111.0 - 2\\2 p000.0 - p000.1 - p001.1 + 3 p010.0 - 2 p010.1 - 2 p011.1 + p101.0 + 2 p110.0 - 2 p110.1 - p111.1 - 1\\2 p000.0 - p000.1 - p001.1 + 3 p010.0 - 2 p010.1 - p011.0 - 2 p011.1 + p101.0 - p110.0 + p110.1 - p111.1 - 1\\2 p000.0 - p000.1 - p001.1 + 3 p010.0 - 2 p010.1 - 2 p011.1 + p101.0 - p111.1 - 1\\p000.1 + p010.1 - p100.0 - p101.0 + 2 p101.1 - 1\\p000.1 + p010.1 - p011.1 - p100.0 - p101.0 + 2 p101.1 + p110.0 - p110.1 - 1\\p000.1 + p010.0 - p100.0 - p101.0 + 2 p101.1 - 1\\2 p000.0 - p000.1 - p001.1 + p010.1 - p011.1 + p101.0 + p110.0 - p110.1 - p111.1 - 1\\2 p000.0 - p000.1 - p001.1 + p010.1 - 2 p011.1 + p101.0 + 2 p110.0 - 2 p110.1 - p111.1 - 1\\2 p000.0 - p000.1 - p001.1 + p010.1 - p011.1 + p101.0 - p111.1 - 1\\2 p000.0 - p000.1 - p001.1 + 2 p010.0 - p010.1 - p011.1 + p101.0 + p110.0 - p110.1 - p111.1 - 1\\2 p000.0 - p000.1 - p001.1 + 2 p010.0 - p010.1 - p011.0 - p011.1 + p101.0 - p110.0 + p110.1 - p111.1 - 1\\2 p000.0 - p000.1 - p001.1 + 2 p010.0 - p010.1 - p011.1 + p101.0 - p111.1 - 1\\p000.1 + p010.1 + p101.1 - 1\\- p001.1 - 2 p011.1 - p100.1 + p110.0 - 2 p110.1 - p111.1\\p000.1 + p010.0 + p101.1 - 1\\p000.1 + p010.0 - p011.0 + p101.1 - p110.0 + p110.1 - 1\\p000.0 + p010.0 + p101.0 - 1\\p000.0 + p010.1 - p011.1 + p101.0 + p110.0 - p110.1 - 1\\p000.0 + p010.1 + p101.0 - 1\\p000.0 + p010.0 - p011.0 + p101.0 - p110.0 + p110.1 - 1\\p000.0 + 2 p010.0 - p010.1 - p011.1 + p101.0 - 1\\p000.0 + 2 p010.0 - p010.1 - p011.0 - p011.1 + p101.0 - p110.0 + p110.1 - 1\\- p001.1 + 2 p010.0 - 2 p010.1 - p011.0 - 2 p011.1 - p100.1 - p110.0 - p111.1\\p000.1 + 2 p010.0 - p010.1 - p011.1 + p101.1 - 1\\p000.1 + 2 p010.0 - p010.1 - p011.1 + p101.1 + p110.0 - p110.1 - 1\\p000.0 + 2 p010.0 - p010.1 - p011.1 + p101.0 + p110.0 - p110.1 - 1
\end{matrix}\right\}

Upper bound

\min\left\{\begin{matrix}
p000.0 + p001.0 - 2 p001.1 + p011.0 - p011.1 - p100.1 - p110.1 + 1\\p000.0 + p001.0 - 2 p001.1 - p100.1 + p101.0 - p101.1 - p110.1 + 1\\p000.0 + p000.1 + p001.0 - p001.1 - p010.0 + 2 p010.1 + p011.1 + p101.0 + 2 p111.1\\p000.0 + p000.1 + p001.0 - p001.1 + p010.1 + p011.0 + p101.0 + p111.1\\- p001.1 - p010.0 + p010.1 - p100.0 - p110.1 + p111.1 + 1\\p000.1 - p001.1 - p100.0 - p101.0 + p101.1 - p110.1 + 1\\- p001.1 - p100.0 - p110.1 + 1\\p000.0 + p001.0 - 2 p001.1 - p100.1 + p101.0 - p101.1 - p110.0 + 1\\p000.1 - p001.1 - p100.0 - p101.0 + p101.1 - p110.0 + 1\\2 p000.1 + p010.0 + p011.1 - p100.0 + p100.1 - p101.0 + 2 p101.1 - p110.0 + p110.1 + p111.0 + p111.1\\p000.1 - p001.1 - p011.0 + p011.1 - p100.0 - p101.0 + p101.1 - p110.0 + 1\\- p001.1 - p100.0 - p110.0 + 1\\p000.1 + p010.0 + p011.1 - p100.0 + p100.1 + p101.1 - p110.0 + p110.1 + p111.0 + p111.1\\p000.1 - p001.1 - p011.0 + p011.1 - p100.0 - p110.0 + 1\\p000.0 + p001.0 - 2 p001.1 - p100.1 - p110.0 + 1\\- p001.0 - p010.0 + p010.1 + p011.1 - 2 p100.0 + p100.1 + p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.1 - p001.0 + p001.1 + p010.0 + 2 p011.1 - 2 p100.0 + 2 p100.1 + 2 p101.1 - 2 p110.0 + 2 p110.1 + p111.0 + 2 p111.1\\- p001.0 + p011.1 - 2 p100.0 + p100.1 + p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\- p001.0 - p010.0 + p010.1 + p011.1 - 2 p100.0 + p100.1 + p101.1 - p110.1 + p111.1 + 1\\- p001.0 + p011.1 - 2 p100.0 + p100.1 + p101.1 - p110.1 + p111.1 + 1\\p000.0 + p001.0 - 2 p001.1 - p010.0 + p010.1 - p100.1 - p110.1 + p111.1 + 1\\p000.0 + p001.0 - 2 p001.1 - p100.1 - p110.1 + 1\\- p001.0 - 2 p010.0 + 2 p010.1 + p011.1 - 2 p100.0 + p100.1 + p101.1 - p110.1 + 2 p111.1 + 1\\- p001.1 - p100.1 - p110.1 + 1\\p000.1 - p010.0 + 2 p010.1 + p011.1 + p101.1 + 2 p111.1\\- p001.0 - p010.0 + p010.1 - p100.0 - p110.1 + p111.1 + 1\\- p001.0 - p100.0 - p110.1 + 1\\p000.1 + p010.0 + p011.1 + p101.1 - p110.0 + p110.1 + p111.0 + p111.1\\- p001.1 - p100.1 - p110.0 + 1\\- p001.0 - p100.0 - p110.0 + 1\\p000.1 - p001.0 + p001.1 + p010.0 + p011.1 - p100.0 + p100.1 + p101.1 - p110.0 + p110.1 + p111.0 + p111.1\\p000.1 + p010.0 + p011.1 + p101.1 - 2 p110.0 + 2 p110.1 + p111.0 + 2 p111.1\\- p001.1 - p100.1 - 2 p110.0 + p110.1 + p111.1 + 1\\- p001.0 - p100.0 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.1 - p001.0 + p001.1 + p010.0 + p011.1 - p100.0 + p100.1 + p101.1 - 2 p110.0 + 2 p110.1 + p111.0 + 2 p111.1\\- p001.0 + p011.1 - 2 p100.0 + p100.1 + p101.1 - 3 p110.0 + 2 p110.1 + 2 p111.1 + 1\\p000.1 - p001.0 + p001.1 + p010.0 + 2 p011.1 - 2 p100.0 + 2 p100.1 + 2 p101.1 - 3 p110.0 + 3 p110.1 + p111.0 + 3 p111.1\\p000.0 + p001.0 - 2 p001.1 - p100.1 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.1 - p001.1 - p011.0 + p011.1 - p100.0 - 3 p110.0 + 2 p110.1 + 2 p111.1 + 1\\p000.1 + p010.0 + p011.1 - p100.0 + p100.1 + p101.1 - 2 p110.0 + 2 p110.1 + p111.0 + 2 p111.1\\- p001.1 - p100.0 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.1 - p001.1 - p011.0 + p011.1 - p100.0 - p101.0 + p101.1 - 3 p110.0 + 2 p110.1 + 2 p111.1 + 1\\2 p000.1 + p010.0 + p011.1 - p100.0 + p100.1 - p101.0 + 2 p101.1 - 2 p110.0 + 2 p110.1 + p111.0 + 2 p111.1\\p000.0 + p001.0 - 2 p001.1 - p100.1 + p101.0 - p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.0 + p000.1 + p001.0 - 2 p001.1 + 2 p011.0 - p011.1 - p101.0 + p101.1 - p110.0 - p111.0 + p111.1 + 1\\p000.1 - 2 p001.1 - p010.0 + p011.0 - p011.1 - p100.0 - p101.1 - 2 p110.0 - 2 p111.0 + p111.1 + 2\\2 p000.0 + 2 p001.0 - 3 p001.1 + p010.0 + 2 p011.0 - 2 p011.1 + p100.0 - p100.1 - p110.1 + 1\\2 p000.0 + p000.1 + 2 p001.0 - 2 p001.1 + p010.0 + p010.1 + 2 p011.0 - p011.1 + p100.0 + 2 p101.0 - p101.1 + p111.1\\p000.0 + p001.0 - 2 p001.1 + p011.0 - p011.1 - p100.1 - p110.0 + 1\\p000.0 + p000.1 + p001.0 - p001.1 - p010.0 + 2 p010.1 + p011.1 + p101.0 - 2 p110.0 + 2 p110.1 + 2 p111.1\\- 2 p001.1 - p010.0 - p011.1 - p100.0 - p100.1 - p101.1 - 2 p110.0 - p111.0 + 2\\- p001.1 - p010.0 + p010.1 - p100.0 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.0 + p001.0 - 2 p001.1 - p010.0 + p010.1 - p100.1 - 2 p110.0 + p110.1 + p111.1 + 1\\- p001.0 - 2 p010.0 + 2 p010.1 + p011.1 - 2 p100.0 + p100.1 + p101.1 - 3 p110.0 + 2 p110.1 + 2 p111.1 + 1\\- p001.1 - p010.0 + p010.1 - p100.1 - 2 p110.0 + p110.1 + p111.1 + 1\\- p001.0 - p010.0 + p010.1 - p100.0 - 2 p110.0 + p110.1 + p111.1 + 1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 + p010.1 + 2 p011.1 + 2 p101.1 + 2 p111.1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 - p010.0 + 2 p010.1 + 2 p011.1 + 2 p101.1 + 2 p111.1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 - 2 p010.0 + 3 p010.1 + 2 p011.1 + 2 p101.1 + 3 p111.1\\p000.1 - 2 p001.0 + p001.1 - p100.0 - p110.1 + 1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 + p010.0 + 2 p011.1 + 2 p101.1 - 2 p110.0 + 2 p110.1 + p111.0 + 2 p111.1\\- p000.0 + p000.1 - p001.0 + p011.1 - p100.1 + p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 - p010.0 + 2 p010.1 + 2 p011.1 + 2 p101.1 - 2 p110.0 + 2 p110.1 + 2 p111.1\\p000.1 - 2 p001.0 + p001.1 - p100.0 - p110.0 + 1\\2 p000.1 - 2 p001.0 + 2 p001.1 + p010.0 + p011.1 - p100.0 + p100.1 + p101.1 - p110.0 + p110.1 + p111.0 + p111.1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 - 2 p010.0 + 3 p010.1 + 2 p011.1 + 2 p101.1 - 3 p110.0 + 3 p110.1 + 3 p111.1\\- p000.0 + 2 p000.1 - p001.0 + p001.1 + p010.0 + 2 p011.1 + 2 p101.1 - 3 p110.0 + 3 p110.1 + p111.0 + 3 p111.1\\- p000.0 + p000.1 - p001.0 + p011.1 - p100.1 + p101.1 - 3 p110.0 + 2 p110.1 + 2 p111.1 + 1\\2 p000.1 - 2 p001.0 + 2 p001.1 + p010.0 + p011.1 - p100.0 + p100.1 + p101.1 - 2 p110.0 + 2 p110.1 + p111.0 + 2 p111.1\\p000.0 - p001.0 + p011.0 - p011.1 - p100.1 - p110.1 + 1\\- p001.0 - p100.1 - p110.1 + 1\\- p001.0 - p010.0 + p010.1 - p100.1 - p110.1 + p111.1 + 1\\p000.0 - p001.0 - p100.1 + p101.0 - p101.1 - p110.1 + 1\\p000.0 + p000.1 - p001.0 + p001.1 - p010.0 + 2 p010.1 + p011.1 + p101.0 + 2 p111.1\\p000.0 + p000.1 - p001.0 + p001.1 + p010.1 + p011.0 + p101.0 + p111.1\\p000.1 - 2 p001.0 + p001.1 - p100.0 - p101.0 + p101.1 - p110.1 + 1\\p000.1 - p001.0 + p001.1 + p010.0 + p011.1 + p101.1 - p110.0 + p110.1 + p111.0 + p111.1\\- p001.0 - p100.1 - p110.0 + 1\\p000.0 - p001.0 - p100.1 + p101.0 - p101.1 - p110.0 + 1\\p000.1 - 2 p001.0 + p001.1 - p100.0 - p101.0 + p101.1 - p110.0 + 1\\- p000.0 + 2 p000.1 - 3 p001.0 + 2 p001.1 - p011.0 + p011.1 - 2 p100.0 + p100.1 - 2 p101.0 + 2 p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.0 + p000.1 - p001.0 + p001.1 + p010.0 + p011.1 + p101.1 + p111.0\\p000.1 - 2 p001.0 + p001.1 - p011.0 + p011.1 - p100.0 - p110.0 + 1\\2 p000.0 - p001.0 + p010.0 + 2 p011.0 - 2 p011.1 + p100.0 - p100.1 - p110.1 + 1\\2 p000.0 + p000.1 - p001.0 + p001.1 + p010.0 + 3 p011.0 - p011.1 + p100.0 + p101.1 + p111.1\\2 p000.0 - p001.0 + p010.0 + 2 p011.0 - 2 p011.1 + p100.0 - p100.1 + 2 p101.0 - 2 p101.1 - p110.1 + 1\\p000.0 + p000.1 - 2 p001.0 + p001.1 + 2 p011.0 - p011.1 + p101.0 - p101.1 - p110.0 - p111.0 + p111.1 + 1\\p000.1 - p001.0 + p001.1 + p010.0 + p011.1 + p101.1 - 2 p110.0 + 2 p110.1 + p111.0 + 2 p111.1\\- p001.0 - p100.1 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.0 - p001.0 - p100.1 + p101.0 - p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\- p000.0 + 2 p000.1 - 3 p001.0 + 2 p001.1 - p011.0 + p011.1 - 2 p100.0 + p100.1 - 2 p101.0 + 2 p101.1 - 3 p110.0 + 2 p110.1 + 2 p111.1 + 1\\p000.1 - 2 p001.0 + p001.1 - p011.0 + p011.1 - p100.0 - 3 p110.0 + 2 p110.1 + 2 p111.1 + 1\\p000.0 - p001.0 + p011.0 - p011.1 - p100.1 - p110.0 + 1\\- p001.0 - p010.0 + p010.1 - p100.1 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.0 - p001.0 - p010.0 + p010.1 - p100.1 + p101.0 - p101.1 - 2 p110.0 + p110.1 + p111.1 + 1\\p000.0 - p001.0 + p011.0 - p011.1 - p100.1 + p101.0 - p101.1 - p110.0 + 1\\p000.1 + p010.1 + p011.1 + p101.1 + p110.0 - p110.1 + p111.0 + p111.1\\p000.1 - p010.0 + 2 p010.1 + p011.1 + p101.1 + p110.0 - p110.1 + p111.0 + 2 p111.1\\2 p000.1 - p001.0 + 2 p001.1 - p010.0 + 3 p010.1 + 2 p011.1 - p100.0 + 2 p100.1 + 2 p101.1 + p110.0 + p111.0 + 3 p111.1 - 1\\2 p000.1 - p001.0 + 2 p001.1 + 2 p010.1 + 2 p011.1 - p100.0 + 2 p100.1 + 2 p101.1 + p110.0 + p111.0 + 2 p111.1 - 1\\2 p000.1 - p001.0 + 2 p001.1 - 2 p010.0 + 4 p010.1 + 3 p011.1 - 2 p100.0 + 3 p100.1 + 3 p101.1 + p110.0 + p111.0 + 4 p111.1 - 1\\2 p000.1 - 2 p010.0 + 3 p010.1 - p011.0 + 2 p011.1 - p100.0 + p100.1 - p101.0 + 2 p101.1 + 3 p111.1\\2 p000.1 - p001.0 + 2 p001.1 - p010.0 + 3 p010.1 + 3 p011.1 - 2 p100.0 + 3 p100.1 + 3 p101.1 + p110.0 + p111.0 + 3 p111.1 - 1\\2 p000.1 + p001.1 + 2 p010.1 + 2 p011.1 - p100.0 + 2 p100.1 + 2 p101.1 + p110.0 + p111.0 + 2 p111.1 - 1\\3 p000.1 + p001.1 + 2 p010.1 + 2 p011.1 - p100.0 + 2 p100.1 - p101.0 + 3 p101.1 + p110.0 + p111.0 + 2 p111.1 - 1\\2 p000.1 + p001.1 - p010.0 + 3 p010.1 + 2 p011.1 - p100.0 + 2 p100.1 + 2 p101.1 + p110.0 + p111.0 + 3 p111.1 - 1\\2 p000.1 - 2 p010.0 + 3 p010.1 - p011.0 + 2 p011.1 - p100.0 + p100.1 + p101.1 + 3 p111.1\\3 p000.1 + p001.1 - p010.0 + 3 p010.1 + 2 p011.1 - p100.0 + 2 p100.1 - p101.0 + 3 p101.1 + p110.0 + p111.0 + 3 p111.1 - 1\\3 p000.1 + p010.1 - p011.0 + 3 p011.1 - p100.0 + 2 p100.1 - 2 p101.0 + 3 p101.1 - p110.0 + p110.1 + p111.1\\2 p000.1 - p001.1 + p010.1 - 2 p011.0 + 2 p011.1 - p100.0 + p100.1 - 2 p101.0 + 2 p101.1 - p110.0 + 1\\3 p000.1 + p010.1 - p011.0 + 3 p011.1 - p100.0 + 2 p100.1 + p101.1 - p110.0 + p110.1 + p111.1\\2 p000.1 - p001.1 + p010.1 - 2 p011.0 + 2 p011.1 - p100.0 + p100.1 - p110.0 + 1\\- p000.0 + 3 p000.1 - p001.0 + 2 p001.1 - p010.0 + 3 p010.1 + 3 p011.1 + p100.1 + 3 p101.1 + p110.0 + p111.0 + 3 p111.1 - 1\\- p000.0 + 3 p000.1 - p001.0 + 2 p001.1 - 2 p010.0 + 4 p010.1 + 3 p011.1 + p100.1 + 3 p101.1 + p110.0 + p111.0 + 4 p111.1 - 1\\3 p000.1 - 2 p001.0 + 3 p001.1 + 2 p010.1 + 2 p011.1 - p100.0 + 2 p100.1 + 2 p101.1 + p110.0 + p111.0 + 2 p111.1 - 1\\- p000.0 + 3 p000.1 - 3 p001.0 + 3 p001.1 - 2 p010.0 + 3 p010.1 - p011.0 + 2 p011.1 - 2 p100.0 + 2 p100.1 - 2 p101.0 + 3 p101.1 + 3 p111.1\\2 p000.1 - p001.0 + 2 p001.1 + 2 p010.1 + 2 p011.1 + p100.1 + 2 p101.1 + p110.0 + p111.0 + 2 p111.1 - 1\\2 p000.1 - p001.0 + 2 p001.1 - p010.0 + 3 p010.1 + 2 p011.1 + p100.1 + 2 p101.1 + p110.0 + p111.0 + 3 p111.1 - 1\\p000.1 - 2 p001.0 + p001.1 - 2 p010.0 + 2 p010.1 - p011.0 + p011.1 - p100.0 - p110.1 + 2 p111.1 + 1\\3 p000.1 - 2 p001.0 + 3 p001.1 - p010.0 + 3 p010.1 + 2 p011.1 - p100.0 + 2 p100.1 + 2 p101.1 + p110.0 + p111.0 + 3 p111.1 - 1\\3 p000.1 - 2 p001.0 + 3 p001.1 + 2 p010.1 + 2 p011.1 - p100.0 + 2 p100.1 - p101.0 + 3 p101.1 + p110.0 + p111.0 + 2 p111.1 - 1\\2 p000.1 - 3 p001.0 + 2 p001.1 + p010.1 - 2 p011.0 + 2 p011.1 - p100.0 + p100.1 - p110.0 + 1\\2 p000.1 - 3 p001.0 + 2 p001.1 + p010.1 - 2 p011.0 + 2 p011.1 - p100.0 + p100.1 - 2 p101.0 + 2 p101.1 - p110.0 + 1\\4 p000.1 - 3 p001.0 + 4 p001.1 + 2 p010.1 - p011.0 + 4 p011.1 - p100.0 + 3 p100.1 - 2 p101.0 + 4 p101.1 - p110.0 + 2 p110.1 + 2 p111.1 - 1\\4 p000.1 - 3 p001.0 + 4 p001.1 + 2 p010.1 - p011.0 + 4 p011.1 - p100.0 + 3 p100.1 + 2 p101.1 - p110.0 + 2 p110.1 + 2 p111.1 - 1\\p000.1 - 2 p001.0 + p001.1 - p011.0 + p011.1 - p100.0 - p110.1 + 1\\p000.1 - 2 p001.0 + p001.1 - p011.0 + p011.1 - p100.0 - p101.0 + p101.1 - p110.1 + 1\\- p000.0 + 3 p000.1 - 3 p001.0 + 3 p001.1 + p010.1 - p011.0 + 2 p011.1 - 2 p100.0 + 2 p100.1 - 2 p101.0 + 3 p101.1 + 2 p111.1\\p000.1 - p001.0 + p001.1 + p010.0 + p011.1 + p101.1 + p110.0 - p110.1 + p111.0 + p111.1\\- p000.0 + 3 p000.1 - 3 p001.0 + 3 p001.1 + p010.1 - p011.0 + 2 p011.1 - 2 p100.0 + 2 p100.1 - p101.0 + 2 p101.1 + 2 p111.1\\- 2 p000.0 + 2 p000.1 - 2 p001.0 + p001.1 - p011.0 + 2 p011.1 - p100.0 - p101.0 + 2 p101.1 - p110.1 + 2 p111.1 + 1\\- p000.0 + 2 p000.1 - 2 p001.0 + 2 p001.1 + p010.1 - p011.0 + 2 p011.1 - 2 p100.0 + 2 p100.1 - p101.0 + 2 p101.1 + 2 p111.1\\p000.1 + p010.0 + p011.1 + p101.1 + p110.0 - p110.1 + p111.0 + p111.1\\- p000.0 + 2 p000.1 - 2 p001.0 + 2 p001.1 + p010.1 - p011.0 + 3 p011.1 - 3 p100.0 + 3 p100.1 - p101.0 + 3 p101.1 + 3 p111.1\\p000.1 - p001.1 - p011.0 + p011.1 - p100.0 - p110.1 + 1\\p000.1 + p010.0 + p011.1 - p100.0 + p100.1 + p101.1 + p110.0 - p110.1 + p111.0 + p111.1\\p000.1 - p001.1 - p011.0 + p011.1 - p100.0 - p101.0 + p101.1 - p110.1 + 1\\- p000.0 + 2 p000.1 - p001.0 - p011.0 + p011.1 - 2 p100.0 + p100.1 - 2 p101.0 + 2 p101.1 - p110.1 + p111.1 + 1
\end{matrix}\right\}