Mutually orthogonal latin squares with large holes [article]

Peter J. Dukes, Christopher M. van Bommel
2014 arXiv   pre-print
Two latin squares are orthogonal if, when they are superimposed, every ordered pair of symbols appears exactly once. This definition extends naturally to 'incomplete' latin squares each having a hole on the same rows, columns, and symbols. If an incomplete latin square of order n has a hole of order m, then it is an easy observation that n > 2m. More generally, if a set of t incomplete mutually orthogonal latin squares of order n have a common hole of order m, then n > (t+1)m. In this article,
more » ... e prove such sets of incomplete squares exist for all n,m ≫ 0 satisfying n > 8(t+1)^2 m.
arXiv:1410.6743v1 fatcat:khupxleg3fbgfaqrifx7yubfgu