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?
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This page created 10 March 2002.