A Better Bound for Locally Thin Set Families

A family of subsets of an n-set is 4-locally thin if for every quadruple of its members the ground set has at least one element contained in exactly 1 of them. We show that such a family has at most 20.4561n members. This improves on our previous results with Noga Alon. The new proof is based on a more careful analysis of the self-similarity of the graph associated with such set families by the graph entropy bounding technique.