Constructing resolvable (v, 3, 3, 2) Lotto designs

Abstract

A (v, k, p, t) Lotto design is a set system (X, B) where |X| = v, B is a collection of k-subsets of X, called blocks, such that, for any p-subset P of X, there exists at least one B ∈ B such that |B ∩ P| ≥ t. Let L(v, k, p, t) denote the minimum number of blocks in any (v, k, p, t) Lotto design. A (v, k, p, t) Lotto design is optimal if it has L(v, k, p, t) blocks. In this paper, we investigate the resolvability of optimal (v, 3, 3, 2) Lotto designs. In addition, we investigate the smallest possible size of (v, 3, 3, 2) resolvable Lotto designs which do not have L(v, k, p, t) blocks.