Covering t-sets with (t+2)-sets

AbstractNew upper bounds for C(v,k,t), the minimum number of k-subsets (blocks) out of a v-set such that each t-subset is contained in at least one block, are obtained by constructing corresponding covering designs with prescribed automorphisms. Computer search with a stochastic heuristic, tabu search, is used to find the covering designs. The new covering designs are listed and a table of upper bounds on C(v,t+2,t) for v⩽28 and t⩽8 is given