Infinite Classes of Covering Numbers

Abstract

AbstractLet D be a family of k-subsets (called blocks) of a v-set X(v). Then D is a (v, k, t) covering design or covering if every t-subset of X(v) is contained in at least one block of D. The number of blocks is the size of the covering, and the minimum size of the covering is called the covering number. In this paper we consider the case t = 2, and find several infinite classes of covering numbers. We also give upper bounds on other classes of covering numbers.