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

Complete Sets of Orthogonal Self-Orthogonal Latin Squares

We show how to produce algebraically a complete orthogonal set of Latin squares from a left quasifield and how to generate algebraically a maximal set of self-orthogonal Latin squares from a left nearfield. For a left Veblen-Wedderburn system, we establish the algebraic relationships between the standard projective plane construction of a complete set of Latin squares, our projective plane cons...

Critical sets for a pair of mutually orthogonal latin squares of odd order greater than 9

Maximal sets of mutually orthogonal Latin squares

Maximal sets of s mutually orthogonal Latin squares of order v are constructed for in nitely many new pairs (s; v). c © 1999 Published by Elsevier Science B.V. All rights reserved

New bounds for pairwise orthogonal diagonal Latin squares

A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. Let dr be the least integer such that for all n > dr there exist r pairwise orthogonal diagonal Latin squares of order n. In a previous paper Wallis and Zhu gave several bounds on the dr. In this paper we shall present some constructions of pairwise orthogonal diagonal Latin squares and conseq...

Lecture 9 : Latin Squares and Geometry Week 9 UCSB