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

✍ Scribed by P.J. Owens; D.A. Preece

• Book ID: 104114077
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 324 KB
• Volume: 167-168
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(97)89938-4

✦ Synopsis

An affine plane of order 9 can be specified by an orthogonal array with l0 constraints and 9 levels. A complete set of pairwise orthogonat 9 x 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 afline 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.