46×46 {-1, +1} matrices of maximal determinant

|Det Rj| = 3663123722407789250099445×245 = 495×1121×245 for j=1, 2 , ..., 17

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

M=RjTRj= Rj RjT for j=1, 2 , ..., 17:

    | S   0 |
M = |       |
    | 0   S |
with S = 44 I + 2 J where I is the 23×23 identity matrix and J is the 23×23 matrix with all entries 1.

There are 17 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:
+++++++++-+-+-++-++---+      ++-++----+++--++-++-+-+
R9:
+++++++++---+-++-+++--+      ++-++---++-+--+-+++-+-+
R10:
+++++++++-++--+-+++---+      ++-++---+++-+-+--+-++-+
R11:
+++++++++---++-+++--+-+      +++--+-+--++--+-+++-+-+
R12:
+++++++++--+-+-+++-+--+      +++-++-+-+++--+--++---+
R13:
+++++++++-+---+-++++--+      +++--+-++-+-+-++--++--+
R14:
+++++++++---+++-++--+-+      +++-++--+-++---++-+-+-+
R15:
++++++++++---+-+++-+--+      ++-+-++-+-++-++--++---+
R16:
++++++++++--+-++-++---+      ++--++-+-+-++-+++-+---+
R17:
++++++++++----+++-++--+      ++--++-+--++-+-++-+-+-+

Notes:

  1. A maximal determinant was first reported by Yang [Y1].
  2. The complete set of 17 inequivalent circulant block forms was found by by Kounias, Koukouvinos, Nikolaou and Kakos [KKNK1].
  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.