Order 29
The conjectured optimal Gram matrix
For order 29 there is a conjectured D-optimal gram matrix G
due to Bruce Solomon (6 July 2002). It is given
here in compressed format,
and in full here
on Will Orrick's website.
The determinant of G is (320*7^12*2^28)^2.
The known H-classes
4918 Hadamard equivalence classes of {+1,-1} solutions R of G = R.R^T = R^T.R
are known. They were found by randomised decomposition of G. For order 29,
switching does not give any new Hadamard equivalence classes.
The complete set of all 4918 known Hadamard equivalence classes is
available here as a gzipped text file.
Of the 4918 H-classes, 336 are self-dual, so there are 2627 HT-classes.
The classes are listed in decreasing order of the automorphism group size.
Group sizes are in {1, 2, 3, 4, 6, 9, 18}.