Previous 29×29 {-1, +1} matrix of largest known determinant

|Det R| = 4360005468315×228 = 45×713×228

Ratio of |Det R| to Barba bound: 0.851485

M=RTR:

 29 -11 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3  1  1  1  1  1  1
-11  29  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
 -3   1 29  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
 -3   1  1 29  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
 -3   1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 29  1  1  1  1  1  1  1
 -3   1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29

M'=R RT:

29  1  1  5  5  5  5  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 1 29  1  5  5  5  5  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 1  1 29  5  5  5  5  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 5  5  5 29  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
 5  5  5  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 5  5  5  1  1 29  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 5  5  5  1  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29  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  1  1 29

R:

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

Notes:

  1. This record was surpassed by the matrix given here.
  2. Cannot achieve Barba bound as 57=2×29-1 is not a perfect square.
  3. This lower bound was reported by Dowdeswell, Neubauer, Solomon and Tumer [DNST].
  4. This is the first case for which the R of largest known determinant does not satisfy RTR=R RT.

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Page created 26 January 2002.
Last modified 6 February 2003.
Comments: maxdet@indiana.edu