Infinite Classes of Covering Numbers

http://dx.doi.org/10.4153/CMB-2000-046-9
Canad. Math. Bull. 43(2000), 385-396

  Published:2000-12-01
 Printed: Dec 2000

Let $D$ 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.