La Jolla Covering Repository

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Ye Olde La Jolla Covering Repository

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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 will be included in the link below.

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LJCR Tables

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Maintained by Dan Gordon