12×12 {-1, +1} matrix of maximal determinant

|Det R| = 1458×211 = 6×35×211

Ratio of |Det R| to Hadamard bound: 1

M=RTR=R RT:

12  0  0  0  0  0  0  0  0  0  0  0
 0 12  0  0  0  0  0  0  0  0  0  0
 0  0 12  0  0  0  0  0  0  0  0  0
 0  0  0 12  0  0  0  0  0  0  0  0
 0  0  0  0 12  0  0  0  0  0  0  0
 0  0  0  0  0 12  0  0  0  0  0  0
 0  0  0  0  0  0 12  0  0  0  0  0
 0  0  0  0  0  0  0 12  0  0  0  0
 0  0  0  0  0  0  0  0 12  0  0  0
 0  0  0  0  0  0  0  0  0 12  0  0
 0  0  0  0  0  0  0  0  0  0 12  0
 0  0  0  0  0  0  0  0  0  0  0 12

R:

++++---+++--
+++-+-+-+-+-
+++--+++---+
+--+--+-----
-+--+--+----
--+--+--+---
-+++------++
+-+-+----+-+
++---+---++-
+------++-++
-+----+-++-+
--+---++-++-

Notes:

  1. Maximal matrix first reported by Hadamard [Had].
  2. Hadamard matrix.
  3. Proved to be unique up to equivalence by Todd [T].

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Page created 26 January 2002.
Last modified 26 January 2003.
Comments: maxdet@indiana.edu