Among the NxN matrices that are the elementwise product (also called Hadamard product) of a circulant sign matrix with a backcirculant sign matrix, examples with maximum |determinant| are as follows. Matrices are specified by the first row of the circulant then the first row of the backcirculant. N det example matrix 1 1.00 -- 2 0.00 +--+ 3 4.00 +++-+- 4 16.00 ++---+-- 5 48.00 ------+--- 6 128.00 +++----+---- 7 512.00 +++++++++-+--- 8 4096.00 ++---+---+------ 9 6912.00 +++++++++++-+++-+- 10 36864.00 +-+++++-+-+++++-++-- 11 273408.00 +++++++++++-+--+++---- 12 -2097152.00 +-+-+--+--+-++-+-++----- 13 14929920.00 +++++++++++++++++-+++--+-+ 14 -50331648.00 ++--+-+--------+-+-+-+-+-+-+