Let $S\subseteq {\mathbb F}_2^u$ have size $n=2^\ell$, and let $h:{\mathbb F}_2^u\to {\mathbb F}_2^\ell$ be a uniformly random linear map. For
$y\in{\mathbb F}_2^\ell$, write ${load}_h(y):=|h^{-1}(y)\cap S|$, and let
$M(S,h):=\max_{y\in{\mathbb F}_2^\ell}\{load}_h(y)$ be the maximum load. Jaber, Kumar and Zuckerman (STOC 2025) proved that the expected maximum load of $h$ on $S$ is ... more >>>