Aspects of complete sets of 9 × 9 pairwise orthogonal latin squares Original Research Article

An affine plane of order 9 can be specified by an orthogonal array with 10 constraints and 9 levels. A complete set of pairwise orthogonal 9 × 9 latin squares is obtained when any two of the constraints are taken as rows and columns. Any 3 of the 10 constraints give rise to an adjugacy set of 9 × 9 latin squares from a particular species. For each of the 7 affine planes of order 9 we count the occurrences of different species amongst the 120 subsets of 3 constraints. We give some properties of these species, including the orders of their automorphism groups. We verify the numbers of subplanes of order 2 in each of the 4 projective planes of order 9.