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 twenty-five 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.