Four pairwise orthogonal latin squares of order 24

AbstractWe improve the lower bound for N(24), the maximum size of a set of parwise orthogonal Latin squares of order 24, from 3 (established in 1960 by Bose and Shrikhande (Trans. Amer. Math. Soc. 95 (1960), 191–209)) to 4. We obtain 7 sets of four squares from 7 sets of 3 pairwise orthogonal orthomorphisms of group Z6 ⊕ Z2 ⊕ Z2 which were found by a non-exhaustive computer search