Some New Maximal Sets of Mutually Orthogonal Latin Squares |
| |
Authors: | P Govaerts D Jungnickel L Storme J A Thas |
| |
Institution: | 1. Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281, B-9000, Gent, Belgium 2. Lehrstuhl für Diskrete Mathematik, Optimierung und Operations Research, Universit?t Augsburg, D-86135, Augsburg, Germany
|
| |
Abstract: | Two ways of constructing maximal sets of mutually orthogonal Latin squares are presented. The first construction uses maximal partial spreads in PG(3, 4) \ PG(3, 2) with r lines, where r ∈ {6, 7}, to construct transversal-free translation nets of order 16 and degree r + 3 and hence maximal sets of r + 1 mutually orthogonal Latin squares of order 16. Thus sets of t MAXMOLS(16) are obtained for two previously open cases, namely for t = 7 and t = 8. The second one uses the (non)existence of spreads and ovoids of hyperbolic quadrics Q + (2m + 1, q), and yields infinite classes of q 2n ? 1 ? 1 MAXMOLS(q 2n ), for n ≥ 2 and q a power of two, and for n = 2 and q a power of three. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|