102×102 {-1, +1} matrix of maximal determinant

|Det R| = 796749514273221923465845850935614091969938499460113234817981719970703125 ×2101 = 2525×2549×2101

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

M=RTR=R RT

    | S   0 |
M = |       |
    | 0   S |
with S = 100 I + 2 J where I is the 51×51 identity matrix and J is the 51×51 matrix with all entries 1.

There is one known matrix, R, composed of circulant blocks, A and B:

 | A   B |
 |       |
 |  T   T|
 |-B   A |
The first rows of A and B are:
R:
+-+-++-+++--+++-+-+-+---+--++++++----++-++-++++-+++      -++++-++++--+-+-+---++-+--++-++-++--+++-----+++++++

Notes:

  1. The maximal matrix, R, was found by Cohn [C2]. It is of circulant block form.
  2. Are there other inequivalent matrices?

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Page created 1 June 2003.
Last modified 1 June 2003.
Comments: maxdet@indiana.edu