Previous 34×34 {-1, +1} matrix of largest known determinant

|Det R| = 7881299347898368×233 = 224×815×233

Ratio of |Det R| to Ehlich/Wojtas bound: 0.848485

M=RTR:

34  2  6  6  6  6  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 2 34  6  6  6  6  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 6  6 34  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 6  6  2 34  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 6  6  2  2 34  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 6  6  2  2  2 34  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2 34  2  2  2  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2 34  2  2  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2  2 34  2  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2  2  2 34  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2  2  2  2 34  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2  2  2  2  2 34  2  2 -2 -2 -2 -2 -2 -2 -2 -2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2  2  2  2  2  2 34  2 -2 -2 -2 -2 -2 -2 -2 -2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2  2  2  2  2  2  2  2 34 -2 -2 -2 -2 -2 -2 -2 -2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2 34  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  2 34  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  2  2 34  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  2  2  2 34  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  2  2  2  2 34  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  2  2  2  2  2 34  2  2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  2  2  2  2  2  2 34  2  0  0  0  0  0  0  0  0  0  0  0  0
 2  2  2  2  2  2 -2 -2 -2 -2 -2 -2 -2 -2  2  2  2  2  2  2  2 34  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 34  2  2  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2 34  2  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2 34  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2 34  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2 34  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2 34  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2 34  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2 34  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2 34  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2 34  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2 34  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2 34

M'=R RT:

34  6  6  6  6  6  6  6 -2 -2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 6 34  2  2  2  2  2  2 -6 -6 -2 -2 -2 -2 -2 -2 -2 -2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 6  2 34  2  2  2  2  2 -6 -6 -2 -2 -2 -2 -2 -2 -2 -2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 6  2  2 34  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 6  2  2  2 34  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 6  2  2  2  2 34  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 6  2  2  2  2  2 34  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 6  2  2  2  2  2  2 34  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
-2 -6 -6  2  2  2  2  2 34  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
-2 -6 -6  2  2  2  2  2  2 34  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 2 -2 -2  2  2  2  2  2  2  2 34  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 2 -2 -2  2  2  2  2  2  2  2  2 34  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 2 -2 -2  2  2  2  2  2  2  2  2  2 34  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 2 -2 -2  2  2  2  2  2  2  2  2  2  2 34  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 2 -2 -2  2  2  2  2  2  2  2  2  2  2  2 34  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 2 -2 -2  2  2  2  2  2  2  2  2  2  2  2  2 34  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 2 -2 -2  2  2  2  2  2  2  2  2  2  2  2  2  2 34  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 2 -2 -2  2  2  2  2  2  2  2  2  2  2  2  2  2  2 34  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 34  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2 34  2  2  2  2  2  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2 34  2  2  2  2  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2 34  2  2  2  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2 34  2  2  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2 34  2  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2 34  2  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2 34  2  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2 34  2  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2 34  2  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2 34  2  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2 34  2  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2 34  2  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2 34  2  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2 34  2
 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2 34

R:

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

Notes:

  1. This determinant has been surpassed by a new record.
  2. Cannot achieve Ehlich/Wojtas bound since 33=34-1 is not the sum of two squares.
  3. This lower bound was reported by Dowdeswell, Neubauer, Solomon and Tumer [DNST].

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Page created 2 March 2002.
Last modified 19 April 2005.