New bounds on Simonyi's conjecture

We say that a pair (A,B) is a recovering pair if A and B are set systems on an n-element ground set, such that for every A,A′∈A and B,B′∈B we have (A∖B=A′∖B′ implies A=A′) and symmetrically (B∖A=B′∖A′ implies B=B′). G. Simonyi conjectured that if (A,B) is a recovering pair, then |A||B|≤2n. For the quantity |A||B| the best known upper bound is 2.3264n due to Holzman and Körner. In this paper we improve this upper bound to 2.2814n.