# 33×33 {-1, +1} matrix of largest known determinant

|Det R| = 1939538511396864×232 = 441×814×232

Ratio of |Det R| to Barba bound: 0.854677

M=RTR=R RT:

```33  9  5  5  5  5  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
9 33  5  1  1  1  1  1  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
5  5 33  1  1  1  1  1  1  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  1  1 33  1  1  1  1  1  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  1  1  1 33  1  1  1  1  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  1  1  1  1 33  1  1  1  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  1  1  1  1  1 33  1  1  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  1  1  1  1  1  1 33  1  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  1  1  1  1  1  1  1 33  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  1  1  1  1  1  1  1  1 33  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  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
1  5  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
1  5  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
1  5  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1
1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33
```

R:

```-+-+++++++----+++++++++++++++++++
++--------+++++++++++++++++++++++
--+--+++++++++++--+++-++-+-++-+++
+-++++++---+-++--+++-+--+--++++++
+-+++++-+-+-+-++-+--+-+-++++-+-++
+-+++-++-++-+---++++++-+-++---+++
+-+++--+++-+-+-+++----++-+++++++-
+--++++-++-++++++--+++--+++-+-+--
+--+++-++++-++--+-+-+++++--+++--+
+-+--+++++++--++++++-++++-+--+---
-++--+++-+++++--++--++--++++++-+-
-+++++---+++++-++-++--+-+-+--++++
-++++-+-+-+++++++++--+-+--+++---+
-++++--++-+++++--+-+++++++---++--
++-+-++++-++-+-++++-+----+---++-+
+++-++-++-+-+-+-+-++-----++++++--
++++-++--+--+++-++-+--++-+--++--+
+++-+-+-++-+-+----+++--+++++-+--+
++++-++-+--++---+-+--+++++-+--++-
++--++-+++-++++--++--++--++----++
++--+++-+++-++-+-+-+-+-+---+-+++-
+++-+-+++---++-++++++-+-+---+--+-
++++--+-+++--++---+-+++---+-++++-
++++-+-+-+--++++-++-+--++-++--+--
++-+++++--++-++-+--++-++--++---+-
++++---++++--++++--+-+--++-+---++
++++-+-++--++--+---+++-+--+-++-++
++-+--+++++++----+-+--+-+-+++-+-+
++++++---+++---+-++++++--+-++----
++-++-++-++++-++--+----+++--++-+-
+++-++--++++--+-++--+--++---+-+++
+++-+-++-+-++-+++---+++----+-++-+
+++-++++--+--+-+-----++++++-+-+-+
```

Notes:

1. Cannot achieve Barba bound as 65=2×33-1 is not a perfect square.
2. This form has not been proved to be optimal.
3. This value was reported by Bruce Solomon on 18 June 2002 and supplants the previous record of 51×815×232 obtained from a maximum excess computation.

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Page created 26 January 2002.