  In 1990, Kolesova, Lam and Thiel determined the 283,657 main classes of Latin
squares of order 8. Using techniques to determine relevant Latin trades and
integer programming, we examine representatives of each of these main classes
and determine that none can contain a uniquely completable set of size less
than 16. In three of these main classes, the use of trades which contain less
than or equal to three rows, columns, or elements does not suffice to determine
this fact. We closely examine properties of representatives of these three main
classes. Writing the main result in Nelder's notation for critical sets, we
prove that scs(8)=16.

Combinatorics