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 $v<100$, $k≤25$, and $t≤8$, just to draw the line somewhere. With a few exceptions, only coverings with at most 100000 blocks are given, to keep the database a reasonable size.

The coverings here have been contributed by over a hundred people around the world over the past thirty years. When the last changes are made to the database, I’ll add a list of the top contributors here.