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

|Det Rj| = 286516723097518282159637789548292042121638501894800×277 for j=1, 2

Ratio of |Det Rj| to Ehlich/Wojtas bound: 0.950654

M=RTR=R RT : 




The matrix is composed of circulant blocks, A and
B:


 | A   B |
 |       |
 |  T   T|
 |-B   A |


The first rows of A and B are:


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




Notes:

    

  1. This determininant surpasses a previous record.

  2. The matrix was found by Tomas Rokicki following
the Lars' Programming Contest.

  3. Cannot achieve Ehlich/Wojtas bound since 77=78-1 is not the sum of two
squares.

  4. This form has not been proved to be optimal.







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Page created 8 April 2005.

Last modified 8 April 2005.

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