A Paley tournament bound for the sensitivity exponent: $2.131121719190$

For every real $\varepsilon>0$ and every integer $S\ge 2$, there are an integer $n\ge 0$ and a total Boolean function $f:\{0,1\}^n\to\{0,1\}$ such that

Here $s(f)$ is the maximum, over all inputs, of the number of individual input bits whose flip changes the output. The block sensitivity $bs(f)$ is the maximum, over all inputs, of the size of a family of pairwise disjoint nonempty sets of input bits, each of whose simultaneous flip changes the output. The number $2.131121719190$ denotes the exact rational $2131121719190/10^{12}$.

The statement uses the campaign's shared definitions of sensitivity, block sensitivity, and SensitivityCampaign.AchievesExponent.