On the Mod-6 Town Rules

Abstract

This note presents an upper bound of $1.252n$ on the size of a set system that satisfies the mod-6 town rules. Under these rules the sizes of the sets are not congruent to $0\mathrm{mod}6$ while the sizes of all pairwise intersections are congruent to $0\mathrm{mod}6$.

Bug. Lemma 1 is incorrect. The lemma needs the sets to be closed under subtraction which they are not