| 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. © 1999 John Wiley & Sons, Inc. J. Combin Designs 7: 217–226, 1999 |
