90×90 {-1, +1} matrices of maximal determinant

|Det R_j| = 10374996594287852916205753173036411405875583423627067060649984×2⁸⁹ = 1958×22⁴³×2⁸⁹

Ratio of |Det R| to Ehlich/Wojtas bound: 1

M=R^TR=R R^T:

    | S   0 |
M = |       |
    | 0   S |

with S = 88 I + 2 J where I is the 45×45 identity matrix and J is the 45×45 matrix with all entries 1.

Notes:

A maximal matrix was first found by Cohn [C1]. It is of circulant block form.
The complete set of 1025 inequivalent circulant block forms was found by by Kounias, Koukouvinos, Nikolaou and Kakos [KKNK2]. A list of these can be obtained from the web page of Christos Koukouvinos.
Are there other inequivalent matrices?

Back to maximal determinant main page.
Page created 28 May 2003.
Last modified 28 May 2003.
Comments: maxdet@indiana.edu