82×82 {-1, +1} matrices of maximal determinant

|Det Rj| = 890604418498560000000000000000000000000000000000000000×281 = 1620×2039×281

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

M=RTR=R RT:

    | S   0 |
M = |       |
    | 0   S |
with S = 80 I + 2 J where I is the 41×41 identity matrix and J is the 41×41 matrix with all entries 1.

Notes:

  1. A maximal matrix can be derived from the maximal matrix of order 41.
  2. The first circulant block construction was found by Cohn [C1].
  3. Four circulant block matrices are listed on Jennifer Seberry's D-optimal design page.
  4. Are there other inequivalent matrices?

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