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Covering design records

Take v points and blocks of k points each. A (v,k,t) covering design is a set of blocks such that every group of t points sits inside at least one block. C(v,k,t) is the fewest blocks that can do it. For most sizes no one knows the exact answer, so public tables keep the best covering anyone has found. Beating an entry means building a valid covering with fewer blocks.

A (v,k,t,m) covering, with m > t, asks less: every set of m points must share at least t points with some block. coveringrepository.com keeps a table of these too, next to the plain coverings that continue the La Jolla Covering Repository.

Our coverings come from a compiled local search that alternates simulated annealing with breakout weighting, and from a bit-parallel search for the (v,k,t,m) tables. Every one is public with a checker that uses plain Python.

35 listed on the public table and 5 reached at the same time by others, who uploaded first.