(This is a related, but different, problem from the previous one for circulants.) A Toeplitz matrix is constant along diagonals. An NxN Toeplitz matrix with entries +-1 and maximum |determinant| is as follows, where I regard the Toeplitz as specified by its entries going up the first column, then rightward along the top row (i.e. "clockwise"). N det example matrix 1 1.00 + 2 2.00 +-- 3 4.00 --+++ 4 16.00 +---+-- 5 48.00 -++++-+++ 6 160.00 +-+++--+--- 7 576.00 -++++-+--++++ 8 2560.00 +-+++---+--+--- 9 12288.00 --+---+++-++-+++- 10 73728.00 ++-++-+++---+--+--- 11 327680.00 +-++++--+++-+-----+-- 12 2097152.00 +-++----+---+-++----+-- 13 14929920.00 -+-+++++-+++--+-+++++-+++ 14 68853760.00 +--+-+-----+++-++-+-+++++--