ON THE NUMBER OF 8X8 LATIN SQUARES

The numbers of non-isomorphic Latin squares of order 8 under the action of various different symmetry groups have been reported by Wells in 1967, by Brown in 1968 and by Arlazarov and coworkers in 1978. The result of Wells has also been independently verified by Bammel and Rothstein in 1975. As an intermediate step towards finding a complete list of projective planes of order 9, we have to generate all the Latin squares of order 8. We find numbers that agree with Wells, but different from those of Brown and Arlazarov and coworkers. These new numbers are reported in this note. We also give the distributions of these numbers according to the size of the automorphism group, which allows one to easily cross check the results. © 1990.