23×23 {-1, +1} matrix of largest known determinant

|Det R| = 662671875×222 = 42411×56×222

Ratio of |Det R| to Ehlich bound: 0.931983

M=RTR=R RT:

23  3  3 -1 -1  3  3 -1 -1 -1 -1 -1 -1  3  3 -1 -1 -1 -1 -1 -1 -1 -1
 3 23  3 -1 -1 -1 -1 -1 -1  3  3 -1 -1  3  3 -1 -1 -1 -1 -1 -1 -1 -1
 3  3 23 -1 -1  3  3 -1 -1  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 23  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1  3 23  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
 3 -1  3  3  3 23  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
 3 -1  3  3  3  3 23 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 23  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1  3 23  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1  3  3 -1 -1 -1 -1  3  3 23  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1  3  3 -1 -1 -1 -1  3  3  3 23 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 23  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 23  3  3 -1 -1 -1 -1 -1 -1 -1 -1
 3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3 23  3 -1 -1 -1 -1 -1 -1 -1 -1
 3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3 23 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 23  3  3  3 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 23  3  3 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3 23  3 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3 23 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 23  3  3  3
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 23  3  3
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3 23  3
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3 23

R:

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

Notes:

  1. Ehlich bound is not achievable as it is not an integer.
  2. This form has not been proved to be optimal.
  3. This lower bound was reported by Dowdeswell, Neubauer, Solomon and Tumer [DNST].
  4. Are M and R unique (up to equivalence)?

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Page created 26 January 2002.
Last modified 11 April 2003.
Comments: maxdet@indiana.edu