In Theorem 36 we saw that it is $\mathsf{NP}$-hard to $(1-\delta_0, 1)$-approximate Max-E$3$Sat for some positive but inexplicit constant $\delta_0$. You might wonder how large $\delta_0$ can be. The natural limit here is $\frac18$ because there is a very simple algorithm which satisfies a $\frac78$-fraction of the constraints in any Max-E$3$Sat instance:

[...]

## Recent comments

Chin Ho Lee: "(The error will be proportional to \sum_i (||X_i||^3 + ||Y_...Avishay Yanay: In the equation of theorem 9, the sum limits are $S\subseteq...Avishay Yanay: #16 What is z^T?F. Mann: The Noise Stability of constant functions have NS=0, as it i...Chin Ho Lee: In Example 42, the first Sel(x_1, x_2, x_2) should be Sel(x_...jake wellens: In Ex. 31 (b), I think we should replace $1/M$ by something ...Grigory Yaroslavtsev: Nice, hope you enjoyed your visit :)