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

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

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

M=RTR=R RT:

    | 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:

  1. A maximal matrix was first found by Cohn [C1]. It is of circulant block form.
  2. 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.
  3. Are there other inequivalent matrices?

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Page created 28 May 2003.
Last modified 28 May 2003.
Comments: maxdet@indiana.edu