40×40 {-1, +1} matrices of maximal determinant

Ratio of |Det R_j| to Hadamard bound: 1

M=R_j^TR_j= R_j R_j^T=40 I
where I is the 40×40 identity matrix.

Notes:

1. Maximal matrix first reported by Hadamard [Had].
2. N. J. A. Sloane's Library of Hadamard matrices has three Hadamard matrices of order 40.
3. The list is presumably not complete.