New constructions of lotto designs

Abstract

An LD(n, k, p, t; b) Lotto Design is a set of b k-sets (blocks) of an n-set such that any p-set intersects at least one k-set in t or more elements. Let L(n, k, p, t) denote the minimum number of blocks in any LD(n, k, p, t; b) Lotto Design. We shall discuss several techniques for constructing Lotto designs and determining upper bounds for L(n, k, p, t).