110×110 {-1, +1} matrices of maximal determinant

|Det Rj| = 21432348501835267584370274029433420674858276152919409595077380293638336640452181×2109 = 2943×2753×2109

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

M=RjTRj=Rj RjT

    | S   0 |
M = |       |
    | 0   S |
with S = 108 I + 2 J where I is the 55×55 identity matrix and J is the 55×55 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 found by Fletcher and Seberry [FS]. They are of circulant block form.

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