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

|Det R| = 4429211904320×228 = 320×712×228

Ratio of |Det R| to Barba bound: 0.865001

M=RTR=R RT:

29  1  1  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  1  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  1 29  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
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
1  1  1  1  1  1 29 -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  1  1  1 -3 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  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. Cannot achieve Barba bound as 57=2×29-1 is not a perfect square.
2. This form has not been proved to be optimal.
3. This value was reported by Bruce Solomon on 6 July 2002. It supersedes his previous record of 45×713×228.

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Page created 26 January 2002.