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

|Det R| = 195910410240×226 = 540×611×226

Ratio of |Det R| to Ehlich bound: 0.956639

M=RTR=R RT:

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

Notes:

  1. This matrix has been surpassed by a new record.
  2. This matrix was discovered by Will Orrick and Bruce Solomon on 20 January 2004 by hill-climbing from a maximal 25×25 determinant augmented with two random rows and columns.
  3. It surpassed the previous record.
  4. Ehlich bound is not achievable as it is not an integer.

Back to maximal determinant main page.
Page created 20 January 2004.
Last modified 12 November 2004.
Comments: maxdet@indiana.edu