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:

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Ohad Klein: In 26, in the "Affine subspace partition" definition, "may b...Ohad Klein: In the very end of prop 12, I think there should be an index...Ohad Klein: In 25 (also in the book) "one one child".Noam Lifshitz: In corollary 17, should it be $\widehat{\mathrm{Maj}_n}(S) =...Ohad Klein: In 49 (56 in the book), it looks like a typo: $E[f_i(y^(j))]...Ryan O'Donnell: Hope so; I'm quite happy with it so far. (Thanks to all who...Yi Zhang: I got it now!!