Problem 724

Let $f(n)$ be the maximum number of mutually orthogonal Latin squares of order $n$ . Is it true that

f(n) \gg n^{1/2}?

Status

Open

No claim settles this problem.

BPS60: Bose, R. C. and Shrikhande, S. S. and Parker, E. T., Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler's conjecture. Canadian J. Math. (1960), 189-203.
Be83c: Beth, Thomas, Eine Bemerkung zur Abschätzung der Anzahl orthogonaler lateinischer Quadrate mittels Siebverfahren. Abh. Math. Sem. Univ. Hamburg (1983), 284-288.
CES60: Chowla, S. and Erdős, P. and Straus, E. G., On the maximal number of pairwise orthogonal Latin squares of a given order. Canadian J. Math. (1960), 204-208.
Wi74: Wilson, Richard M., Concerning the number of mutually orthogonal Latin squares. Discrete Math. (1974), 181-198.