118×118 {-1, +1} matrices of maximal determinant

|Det R_j| = 771382425192890776770216007362197820630031276881559375545475843907812376207883842053437×2¹¹⁷ = 3393×29⁵⁷×2¹¹⁷

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

M=R_j^TR_j=R_j R_j^T

    | S   0 |
M = |       |
    | 0   S |

with S = 116 I + 2 J where I is the 59×59 identity matrix and J is the 59×59 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:

The maximal matrices R₁ and R₂ were found by Fletcher, Koukouvinos, and Seberry [FKS]. They are of circulant block form.

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