16×16 {-1, +1} matrices of maximal determinant

|Det Rj| = 131072×215 = 8×47×215 for j=1, 2, 3, 4, 5

Ratio of |Det Rj| to Hadamard bound: 1

M=RjTRj= Rj RjT for j=1, 2, 3, 4, 5:

16  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0 16  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0 16  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0 16  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  0 16  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  0  0 16  0  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0 16  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  0 16  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0 16  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0 16  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0 16  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0 16  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0 16  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  0 16  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  0  0 16  0
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 16

R1:

++++++++++++++++
+-+-+-+-+-+-+-+-
++--++--++--++--
+--++--++--++--+
++++----++++----
+-+--+-++-+--+-+
++----++++----++
+--+-++-+--+-++-
++++++++--------
+-+-+-+--+-+-+-+
++--++----++--++
+--++--+-++--++-
++++--------++++
+-+--+-+-+-++-+-
++----++--++++--
+--+-++--++-+--+
R2:
++++++++++++++++
+-+-+-+-+-+-+-+-
++--++--++--++--
+--++--++--++--+
++++----++++----
+-+--+-++-+--+-+
++----++++----++
+--+-++-+--+-++-
++++++++--------
+-+-+--+-+-+-++-
++--++----++--++
+--++-+--++--+-+
++++--------++++
+-+--++--+-++--+
++----++--++++--
+--+-+-+-++-+-+-
R3:
++++++++++++++++
+-+-+-+-+-+-+-+-
++--++--++--++--
+--++--++--++--+
++++----++++----
+-+--+-++-+--+-+
++----++++----++
+--+-++-+--+-++-
++++++++--------
++++--------++++
++--+-+---++-+-+
++---+-+--+++-+-
+-+-+--+-+-+-++-
+-+--++--+-++--+
+--+++---++---++
+--+--++-++-++--
R4:
++++++++++++++++
+-+-+-+-+-+-+-+-
++--++--++--++--
+--++--++--++--+
++++----++++----
+-+--+-++-+--+-+
++----++++----++
+--+-++-+--+-++-
++++++++--------
+++-+------+-+++
++-+---+--+-+++-
++---++---+++--+
+-++-+---+--+-++
+-+---++-+-+++--
+--++-+--++--+-+
+---++-+-+++--+-
R5:
++++++++++++++++
+-+-+-+-++++----
++--++--++--++--
+--++--++-+-+-+-
++++----++----++
+-+--+-++--++--+
++----+++--+-++-
+--+-++-+-+--+-+
++++++++--------
+-+-+-+-----++++
++--++----++--++
+--++--+-+-+-+-+
++++------++++--
+-+--+-+-++--++-
++----++-++-+--+
+--+-++--+-++-+-

Notes:

  1. These matrices taken from N. J. A. Sloane's Library of Hadamard matrices.
  2. Maximal matrix first reported by Sylvester [Sy].
  3. R1 is a Sylvester matrix.
  4. The set of five inequivalent matrices Rj is complete [T].

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