On $2$-parent-identifying set systems of block size $4$

Abstract

Parent-identifying set system is a kind of combinatorial structures with applications to broadcast encryption. In this paper we investigate the maximum number of blocks I2(n, 4) in a 2-parentidentifying set system with ground set size n and block size 4. The previous best known lower bound states that I2(n, 4) = Ω(n 4/3+o(1) ). We improve this lower bound by showing that I2(n, 4) = Ω(n 3/2−o(1) ) using techniques in additive number theory.