New constructions for covering designs

A( v , k, t ) covering design , or covering , is a family of k ‐subnets, called blocks , chosen from a v ‐set, such that each t ‐subnet is contained in at least one of the blocks. The number of blocks is the covering's size , and the minimum size of such a covering is denoted by C(v,k,t) . This paper gives three new methods for constructing good coverings; a greedy algorithm similar to Conway and Sloane's algorithm for lexicographic codes [6], and two methods that synthesize new coverings from preexisting ones. Using these new methods, together with results in the literature, we build tables of upper bounds on C(v,k,t) for v ⩽ 32, k ⩽ 16, and t ⩽ 8.