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}.