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

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 paper, a computer search for nding 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 nd 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.