Infinite Classes of Covering Numbers

Abstract Let $D$ be a family of $k$ -subsets (called blocks) of a $v$ -set $X\left( v \right)$ . Then $D$ is a $\left( v,\,k,\,t \right)$ covering design or covering if every $t$ -subset of $X\left( v \right)$ 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.