70×70 {-1, +1} matrices of largest known determinant

|Det R_j| = 46534198660232702315328376954951333913138372×2⁶⁹ = 1156×17³³×2⁶⁹

Ratio of |Det R_j| to Ehlich/Wojtas bound: 0.985507

M=R_j^TR_j= R_j R_j^T:

R_j:
The matrices of have the form

 | X   J   K |
 |           |
 |  T        |
 | J   A   B |
 |           |
 |  T   T   T|
 | K  -B   A |

where X is an arbitrary 2×2 matrix, J is a 2×34 matrix of 1s, K is a 2×34 matrix of the form

 ++++++...+
 ------...-

and A and B are 34×34 circulant matrices.

There are many choices for the first rows of A and B, of which one example is given:
a₁, b₁:

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

Notes:

Cannot achieve Ehlich/Wojtas bound since 69=70-1 is not the sum of two squares.
This form has not been proved to be optimal.
This determinant was discovered by Will Orrick and Tomas Rokicki in April 2005; it surpasses an old record.

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Page created 3 October 2012.
Last modified 3 October 2012.
Comments: maxdet@indiana.edu