8×8 {-1, +1} matrix of maximal determinant

|Det R| = 32×27 = 4×23×27

Ratio of |Det R| to Hadamard bound: 1

M=RTR=R RT:

8 0 0 0 0 0 0 0
0 8 0 0 0 0 0 0
0 0 8 0 0 0 0 0
0 0 0 8 0 0 0 0
0 0 0 0 8 0 0 0
0 0 0 0 0 8 0 0
0 0 0 0 0 0 8 0
0 0 0 0 0 0 0 8

R:

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

Notes:

  1. Maximal matrix first reported by Sylvester [Sy].
  2. Hadamard matrix.
  3. Sylvester matrix.
  4. R is unique up to equivalence.

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