78×78 {-1, +1} matrix of largest known determinant

|Det R| = 290423259051098009373563569569792000000000000000000×277 = 37×761×(18×20)18×277

Ratio of |Det R| to Ehlich/Wojtas bound: 0.963616

M=RTR= R RT:


R:
The matrix has the form

 | X   J   K |
 |           |
 |  T        |
 | J   A   B |
 |           |
 |  T   T   T|
 | K   B  -A |
where X is the 2×2 matrix
++
+-,
J is the 2×38 matrix of 1s, K is the 2×38 matrix
 ++++++...+
 ------...-,
and A and B are 38×38 circulant matrices.

The first rows of A and B are:
a, b:

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

Notes:

  1. Cannot achieve Ehlich/Wojtas bound since 77=78-1 is not the sum of two squares.
  2. This form has not been proved to be optimal.
  3. This determinant was discovered by Tomas Rokicki in April 2005 following Lars Backstrom's programming contest; it surpasses an old record.

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Page created 5 October 2012.
Last modified 5 October 2012.
Comments: maxdet@indiana.edu