Classification of generalized hadamard matrices H(6, 3) and quaternary hermitian self-dual codes of length 18

All generalized Hadamard matrices of order 18 over a group of order 3, H(6, 3), are enumerated in two different ways: once, as class regular symmetric (6, 3)-nets, or symmetric transversal designs on 54 points and 54 blocks with a group of order 3 acting semi-regularly on points and blocks, and secondly, as collections of full weight vectors in quaternary Hermitian self-dual codes of length 18. The second enumeration is based on the classification of Hermitian self-dual [18, 9] codes over GF(4), completed in this paper. It is shown that up to monomial equivalence, there are 85 generalized Hadamard matrices H(6, 3), and 245 inequivalent Hermitian self- dual codes of length 18 over GF(4).