# 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.