114×114 {-1, +1} matrices of maximal determinant

|Det Rj| = 124144704376987147591090863696943577236908775045646724444758251107277947338278043648×2113 = 3164×2855×2113

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

M=RjTRj=Rj RjT

    | S   0 |
M = |       |
    | 0   S |
with S = 112 I + 2 J where I is the 56×56 identity matrix and J is the 56×56 matrix with all entries 1.

There are two known matrices composed of circulant blocks, A and B:

 | A   B |
 |       |
 |  T   T|
 |-B   A |
The first rows of A and B are:
R1:
-++----++---+-++--+---+-+--+--------+---++------+++++-+-+
+---+++--+++-+--++--+--+-++-+-++--++-+-+--++++++-------+-
R2:
------+-+++--+-+------++------+---+----++-+-++-++-+++---+
+++-++-+---++-+-+++-+---+++++--+---+++---+-+--+--+----++-

Notes:

  1. The maximal matrices R1 and R2 were constructed by Koukouvinos, Kounias, and Seberry [KKS]. They are of circulant block form.

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Page created 12 April 2005.
Last modified 12 April 2005.
Comments: maxdet@indiana.edu