38×38 {-1, +1} matrices of maximal determinant

|Det Rj| = 5553501505988967477×237 = 333×917×237 for j=1, 2 , ..., 8

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

M=RjTRj= Rj RjT for j=1, 2 , ..., 8: 

    | S   0 |
M = |       |
    | 0   S |
with S = 36 I + 2 J where I is the 19×19 identity matrix and J is the 19×19 matrix with all entries 1.

There are eight inequivalent matrices composed of circulant blocks, A and B:

 | A   B |
 |       |
 |  T   T|
 |-B   A |
The first rows of A and B are:
R1: 
+++++---+-++-++++-+      +++--+--+++-+-+++-+
R2: 
+++++---+-++-++++-+      ++++--+++-+-+--++-+
R3: 
++++++---+-+-++++-+      +++--+++-++-++--+-+
R4: 
++++++-++-++--+-+-+      +++++---++-+-+++--+
R5: 
++++++---++-++-++-+      +++++--+++--+-+-+-+
R6: 
+++++++-+--+++--+-+      +++--+--+++-+-+++-+
R7: 
+++++++-+--+++--+-+      ++++--+++-+-+--++-+
R8: 
++++++++--++-+-+--+      +++--+-+++-+--+++-+

Notes:

  1. A maximal determinant was first reported by Ehlich [E1].
  2. The complete set of circulant block forms was found by Yang [Y3]. That there are eight inequivalent ones was shown by Kounias, Koukouvinos, Nikolaou and Kakos [KKNK1] who gave the forms listed here.
  3. Are there other inequivalent matrices not in the form of circulant blocks?
Back to maximal determinant main page.
This page created 10 March 2002.