32×32 {-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=32 I
where I is the 32×32 identity matrix.

Notes:

1. Maximal matrix first reported by Sylvester [Sy].
2. For a list of 22 Hadamard matrices of order 32, refer to Jennifer Seberry's home page.
3. The list is not complete.