A (28,13,4) covering design with 53 blocks

A (28,13,4) covering design with 53 blocks, improving the best known upper bound on the covering number C(28,13,4) from 54 to 53. A (v,k,t)-covering design is a collection of k-element subsets (blocks) of {1,...,v} such that every t-element subset is contained in at least one block. C(v,k,t) is the minimum number of blocks required. This design covers all 20,475 four-element subsets of {1,...,28} using 53 blocks of size 13. The previous best known value of 54 blocks was found by Kamal Fadlaoui on 22 September 2008. The Schonheim lower bound is 39, so C(28,13,4) lies in [39,53]. The design was found by local search with dynamic constraint weighting, starting from the known 54-block design with one block deleted. It was verified by two independently written programs, both confirming all 20,475 four-subsets are covered by 53 distinct blocks. Includes the design, an independent verifier so that anyone can check the result, and the previous 54-block design for comparison. The search program itself is not published; the method is described in the accompanying README. SHA-256 of C28_13_4_53blocks.txt:05515bc80397f76dd0342f888ff79a3a4830a7f3327bdec474da93a23c3d1d6c