General Upper Bounds on the Minimum Size of Covering Designs

LetDbe a finite family ofk-subsets (called blocks) of av-setX(v). ThenDis a (v, k, t) covering design or covering if everyt-subset ofX(v) is contained in at least one block ofD. 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 find new upper bounds on the covering numbers for several families of parameters.