The maximal {-1,1}-determinant of order 15

Abstract

We demonstrate the D-optimality of the 15×15 −1,1-matrix discovered independently by Smith and Cohn. This matrix has determinant 25515×2¹⁴ and is unique up to Hadamard equivalence. In addition, we confirm the previously established values of the maximal determinant for all other odd orders up to 21, excluding 19, and we improve the upper bounds on the maximal determinant in orders 29, 33, and 37.