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

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

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 = 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:

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

Back to maximal determinant main page.
Page created 12 April 2005.
Last modified 12 April 2005.
Comments: maxdet@indiana.edu