56×56 {-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=56 I
where I is the 56×56 identity matrix.

Notes:

1. Maximal matrix first reported by Paley [P].
2. N. J. A. Sloane's Library of Hadamard matrices has two Hadamard matrices of order 56.
3. The list is presumably not complete.