Upper bounds on the general covering number Cλ(v, k, t, m)

Abstract

AbstractA collection $\cal C$ of k‐subsets (called blocks) of a v‐set X (v) = {1, 2,…, v} (with elements called points) is called a t‐(v, k, m, λ) covering if for every m‐subset M of X (v) there is a subcollection $\cal K$ of $\cal C$ with $|\cal K|\geq \lambda$ such that every block K ∈ $\cal K$ has at least t points in common with M. It is required that v ≥ k ≥ t and v ≥ m ≥ t. The minimum number of blocks in a t‐(v, k, m, λ) covering is denoted by Cλ(v, k, t, m). We present some constructions producing the best known upper bounds on Cλ(v, k, t, m) for k = 6, a parameter of interest to lottery players. © 2004 Wiley Periodicals, Inc.