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 years. See the acknowledgements page for some of their names, and links to other sites about covering designs.

### Search for Covering Designs