Previous 27×27 {-1, +1} matrix of largest known determinant

|Det R| = 187928875008×226 = 518×611×226

Ratio of |Det R| to Ehlich bound: 0.917665

M=RTR=R RT:

27  3  3  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
 3 27  3  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
 3  3 27  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
 3  3  3 27  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
 3  3  3  3 27  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 -1 -1 -1 -1 -1 -1
 3  3  3  3  3 27 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 -1 -1 -1 -1 -1 -1
 3  3  3  3 -1 -1 27 -1 -1 -1 -1  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 27  3  3  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1  3 27  3  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1  3  3 27  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1  3  3  3 27  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1  3  3  3  3  3 27  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1  3  3  3  3  3  3 27 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1  3  3  3  3 -1 -1 27 -1 -1 -1 -1  3  3 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 27  3  3  3  3  3  3 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 27  3  3  3  3  3 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3 27  3  3  3  3 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3 27  3  3  3 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3  3  3 27  3 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3  3  3  3 27 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1  3  3 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3  3 -1 -1 27 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 27  3  3  3  3  3
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 27  3  3  3  3
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3 27  3  3  3
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3 27  3  3
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3  3 27  3
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3  3  3 27
R:
-++-+--++--+-+++++++++--+-+
--++-+--+-+-+++++++++-+++--
++---+-+-+--+++++++++--+-++
+--++----+++-++++++++++--+-
-+-+--++--+---++++++----++-
+-+---+-++----++++++--+---+
----++-++++---++++--++-+---
-+-++-+++++++++--++---++--+
-++--+++++++++-++-+--++--+-
+-+-+-++++++++-+-+-+---+++-
+--+-++++++++++-+--+-+--+-+
++-----++++++---++--+-+-+--
--++---++++++-++----+----++
++++---++++--+----++-+-+---
+++++++-++--+-+--++-++--++-
+++++++++--+--+-+--++-++-+-
++++++++--+-+--+-+-++++---+
+++++++--+++---++-+-+--++-+
++++++--+-+--+--++-------++
++++++-+-+---+++------+-+--
++++--+----++-++++---+-+---
+-+-+--+--+-+-+-+-+--++++++
-+-++---++--+--++--+-++++++
-++--+---+++--+--+-+-++++++
--++--++-+---+--++--+++++++
++----+-+-+--+++----+++++++
+--+-+-++--+---+-++--++++++

Notes:

  1. This determinant has been superseded by a new record.
  2. R was given in [OSDS] and surpasses the previous record.
  3. Ehlich bound is not achievable as it is not an integer.

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Page created 6 February 2003.
Last modified 20 January 2004.
Comments: maxdet@indiana.edu