论文信息 - Aspects of complete sets of 9 × 9 pairwise orthogonal latin squares

Aspects of complete sets of 9 × 9 pairwise orthogonal latin squares

Abstract 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.

P. J. Owens | Donald A. Preece | Peter J. Owens | D. Preece

[1] C. Colbourn,et al. The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.

[2] J. Dénes,et al. Latin squares and their applications , 1974 .

[3] H. W. Norton. THE 7 × 7 SQUARES , 1939 .

[4] P. J. Owens,et al. Complete Sets of Pairwise Orthogonal Latin Squares and the Corresponding Projective Planes , 1992, J. Comb. Theory, Ser. A.