Ratio of |Det R| to Ehlich/Wojtas bound: 0.969522

M=R^{T}R=
R R^{T}:

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 2×46 matrix of 1s, K is the 2×46 matrix

++++++...+ ------...-,and A and B are 46×46 circulant matrices.

The first rows of A and B are:

a, b:

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

Notes:

- Cannot achieve Ehlich/Wojtas bound since 93=94-1 is not the sum of two squares.
- This form has not been proved to be optimal.
- 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