Mutually nearly orthogonal Latin squares of order 6

Abstract

Raghavarao, Shrikhande and Shrikhande (2001) defined two Latin squares of even order v to be mutually nearly orthogonal if, when superimposed, the squares form a v × v array of ordered pairs such that the number of occurrences of the ordered pair (i, j) is 0 if i = j, is 2 if i - j ≡ v/2 (mod v), and is 1 otherwise. They gave the upper bound (v/2) + 1 for the number of mutually nearly orthogonal Latin squares if v ≡ 2 (mod 4). We show that this upper bound is not attainable for v = 6.