On Symmetric Transversal Designs STD8[24; 3]'s

الملخص EN

The existence of a class regular symmetric transversal design STDλ[3λ;3] is equivalent to a generalized Hadamard matrix of order 3u over GF(3).

Let nλ be the number of nonisomorphic STDλ[3λ;3]'s.

It is known that n1=1, n2=1, n3=4, n4=1, n5=0, n6≥20, and n7≥5.

In this paper, it is shown that n8≥24.