General Upper Bounds for Covering Numbers

Abstract

A $t$-(n, k, $\lambda$) covering design consists of a collection of $k$-element subsets (blocks) of an $n$-element set $\chi$ such that each $t$-element subset of $\chi$ occurs in at least $\lambda$ blocks. We use probabilistic techniques to obtain a general upper bound for the minimum size of such designs, extending a result of Erdős and Spencer [4].