Abstract
AbstractA Room n-cube of side t is an n dimensional array of side t which satisfies the property that each two dimensional projection is a Room square. The existence of a Room n-cube of side t is equivalent to the existence of n pairwise orthgonal symmetric Latin squares (POSLS) of side t. The existence of n pairwise orthogonal starters of order t implies the existence of n POSLS of side t. Denote by v(n) the maximum number of POSLS of side t. In this paper, we use Galois fields and computer constructions to construct sets of pairwise orthogonal starters of order t ≤ 101. The existence of these sets of starters gives improved lower bounds for v(n). In particular, we show v(17) ≥ 5, v(21) ≥ 5, v(29) ≥ 13, v(37) ≥ 15 and v(41) ≥ 9, among others.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics,Statistics and Probability
Cited by
15 articles.
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