Closing a gap in the spectrum of critical sets

In 1998 Donovan and Howse proved that for all n there exist critical sets of order n and size s, where l rt J ~ s ~ n2;n with the exception of the case s = rt + 1 when n is even. In this paper we will present a construction for this case, where n :2: 6, based on the discovery of a critical set of size 17 for a Latin square of order 8. This verifies that there does exist a critical set of order n and size rt + 1 when n is even.