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 database 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 $v \leq 100$, $k \leq 25$, and $t≤8$, just to draw the line somewhere. With a few exceptions, only coverings with at most $150,000$ blocks are given, to keep the database a reasonable size.

The coverings were contributed by over a hundred people around the world over the past thirty years. You may see information about the top contributors here.

Giovanni Acerbi’s website coveringrepository.com has similar functionality to my old website, and in addition to all the coverings in this database, contains more recent improvements and more general $(v,k,t,m)$-covering designs.

The 1996 paper that started all this gave bounds without actually constructing the covering designs. It had a few errors, listed here.