K5(7,3)⩽100

One of the main aims in the theory of covering codes is to obtain good estimates on Kq(n,R), the minimal cardinality of an R-covering code over the nth power of an alphabet with q elements. This paper reports on the new bound K5(7,3)⩽100, obtained by an improved computer search based on Östergård and Weakleyʹs method. In particular, the code leading to this bound has a group of automorphisms quite different from the one Östergård and Weakley used. This new upper bound significantly improves the former record (which was 125).