A (v,k,t)-covering design is a collection of k-element subsets, called blocks, of {1,2,…,v}, such that any t-element subset is contained in at least one block. This site contains a collection of good (v,k,t)-coverings. Each of these coverings gives an upper bound for the corresponding C(v,k,t), the smallest possible number of blocks in such a covering design.
The limit for coverings is v<100, k≤25, and t≤8, just to draw the line somewhere. Only coverings with at most 100000 blocks are given, except for some which were grandfathered in. Some Steiner systems (coverings in which every t-set is covered exactly once) which are too big for the database are given at the Steiner Systems link above.
The coverings here have been contributed by over a hundred people around the world over the past thirty years. See the acknowledgements page for some of their names, and links to other sites about covering designs.
This annotated bibliography gives a few references to results in the literature which contributed to the covering designs and bounds on this site.
Alert!
See the announcement on my home page. This website will be shutting down in 2026, and after March 1 no new covering designs will be accepted.