Previous 35×35 {-1, +1} matrices of largest known determinant

|Det Rj| = 34277093385716188×234 for j=1, 2

Ratio of |Det Rj| to Ehlich/Wojtas bound: 0.858768

M=RjTRj= Rj RjT for j=1, 2:

 35  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
  3 35  3 -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 -1 -1 -1 
  3  3 35  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 -1 -1 -1 -1 -1 -1 -1 
  3 -1  3 35  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 -1 -1 -1 -1 -1 -1 
  3 -1 -1  3 35  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 -1 -1 -1 -1 -1 
  3 -1 -1 -1  3 35  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 -1 -1 -1 -1 
  3 -1 -1 -1 -1  3 35  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 -1 -1 -1 
  3 -1 -1 -1 -1 -1  3 35  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 -1 -1 
  3 -1 -1 -1 -1 -1 -1  3 35  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 -1 
  3 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1  3 35  3 -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 -1 -1 -1 -1  3 35  3 -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 -1 -1 -1 -1  3 35  3 -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 -1 -1 -1 -1  3 35  3 -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 -1 -1 -1 -1  3 35  3 -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 -1 -1 -1 -1  3 35  3 -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 -1 -1 -1 -1  3 35  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 35  3 -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 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  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 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 35  3 
 -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 -1 -1 -1 -1  3 35 

There are 2 known inequivalent matrices composed of 17×17 circulant blocks, A and B,

 |-1   j  -j |
 |           |
 |  T        |
 | j   A   B |
 |           |
 |  T   T   T|
 |-j   B  -A |
where j is the 1×17 all 1 vector.

The first rows of A and B are:
R1:

++--+---+-+-++-++      +-----++----+++-+
R2:
----++++--++-++-+      -++--+++-+-+-----

Notes:

  1. This determinant has been surpassed by a new record.
  2. This determininant surpasses a previous record. It was discovered by Tomas Rokicki.
  3. The matrix R1 was found by Tomas Rokicki during the Lars' Programming Contest. R2 was independently found by Ivan Kazmenko and Vadim Trofimov during the same contest. The same determinant value was also found by Jean-Charles Meyrignac and Jaroslaw Wroblewski, again as part of the Lars' contest. To force M=RRT to have the given form, we have decimated the rows as they were given by their original discoverers.
  4. Transposing the above matrices gives 2 additional inequivalent matrices.
  5. Cannot achieve Ehlich bound since it is not an integer.
  6. This form has not been proved to be optimal.

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Page created 19 April 2005.
Last modified 2 October 2012.
Comments: maxdet@indiana.edu