30×30 {-1, +1} matrices of maximal determinant

|Det Rj| = 19668469112621×229 = 203×713×229 for j=1, 2 , 3

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

M=RjTRj= Rj RjT for j=1, 2 , 3:

    | S   0 |
M = |       |
    | 0   S |
with S = 28 I + 2 J where I is the 15×15 identity matrix and J is the 15×15 matrix with all entries 1.

There are three 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:
+++++++--++-+-+      ++++--++-+-+--+

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 three 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?

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This page created 10 March 2002.