1995/02/16 by Daniel Gordon, Greg Kuperberg, Oren Patashnik · 1 citation
Mathematics · #math.CO
published as J. Combin. Des. 4 (1995), no. 4, 269-284
arxiv created 1995/02/16 · arxiv updated 2009/12/01
A (v,k,t) \em covering design, or \em covering, is a family of k-subsets, called blocks, chosen from a v-set, such that each t-subset is contained in at least one of the blocks. The number of blocks is the covering's \em 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~\citelex, 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.%