44×44 {-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=44 I
where I is the 44×44 identity matrix.

Notes:

1. Maximal matrix first reported by Paley [P].
2. Svetlana Topalova has classified the Hadamard matrices of order 44 with automorphisms of order 7 and found their number to be 384 [To]. They are available from her web page.
3. Christos Koukouvinos has files of 6018 Hadamard matrices and 784 skew-Hadamard matrices on his home page. Jennifer Seberry's web site lists a Williamson-type Hadamard matrix of order 44.