Published online by Cambridge University Press: 20 November 2018
Let n = 4t +- 2, where the integer t ≧ 2. A necessary condition is given for a particular Latin square L of order n to have a complete set of n — 2 mutually orthogonal Latin squares, each orthogonal to L. This condition extends constraints due to Mann concerning the existence of a Latin square orthogonal to a given Latin square.