General upper bounds on the minimum size of covering designs

Let D be a finite 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 t he covering, and the minimum size of the covering is called the covering nu mber. In this paper we find new upper bounds on the covering numbers for se veral families of parameters. (C) 1999 Academic Press.