Covering Designs

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.

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