Title: New coverings of t-sets with (t+1)-sets

Published in: Journal of Combinatorial Designs 7 (1999), 217--226

Abstract: The minimum number of k-subsets out of a v-set such that each t-set is contained in at least one k-set is denoted by C(v,k,t). In this article, a computer search for finding good such covering designs, leading to new upper bounds on C(v,k,t), is considered. The search is facilitated by predetermining automorphisms of desired covering designs. A stochastic heuristic search (embedded in the general framework of tabu search) is then used to find appropriate sets of orbits. A table of upper bounds on C(v,t+1,t) for v <= 28 and t <= 8 is given, and the new covering designs are listed.