Ratio of |Det R_{j}| to Ehlich/Wojtas bound:
0.990476

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 2×52 matrix of 1s, K is a 2×52 matrix of the form

++++++...+ ------...-and A and B are 52×52 circulant matrices.

There are 3 known choices for the first rows of A and B:

a_{1}, b_{1}:

+++++++-+-+-+-+-++-++-+--+-+-++-+---++-----+----++-- +--++--+-++-+++---+-+++-----+++++-+++-----++--++--+-a

+++++++-+++-+-+-+---++--+----+-+--++--+-++--++-+---- +-+++--+----+-+++--++-+--+--+-+-+++------++++--++++-a

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

Notes:

- Cannot achieve Ehlich/Wojtas bound since 105=106-1 is not the sum of two squares.
- This form has not been proved to be optimal.
- This determinant was discovered by Will Orrick on 24 April 2005.
- From the row-pairs above, 60 inequivalent matrices can be obtained by modifying the corner, X, and by transposition.

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Page created 24 April 2005.

Last modified 26 April 2005.

Comments: maxdet@indiana.edu