Order 27

The conjectured optimal Gram matrix

For order 27 there is a conjectured D-optimal gram matrix G due to Hiroki Tamura (26 August 2005). It is given here in compressed format, and in full here on Will Orrick's website.

The determinant of G is (546*6^11*2^26)^2.

Generators for 204 ST-classes

Generators for the 204 known ST-classes are given here. From these generators one can find 6489 HT-classes of maxdet matrices using the operations of row/column switching and taking duals (transposes). This gives 12911 Hadamard equivalence classes of solutions with determinant 546*6^11*2^26.

All 12911 H-classes of solutions

The complete set of all 12911 known Hadamard equivalence classes is available here as a gzipped text file.