Ratio of |Det R_{j}| to Ehlich/Wojtas bound:
0.985507

M=R_{j}^{T}R_{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:

a_{1}, b_{1}:

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

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