International Journal of Combinatorics
Volume 2010 (2010), Article ID 821078, 14 pages
doi:10.1155/2010/821078
Research Article

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

Teppei Hatono and Chihiro Suetake

Department of Mathematics, Faculty of Engineering, Oita University, Oita 870-1192, Japan

Received 20 January 2010; Accepted 17 March 2010

Academic Editor: Laszlo A. Szekely

Copyright © 2010 Teppei Hatono and Chihiro Suetake. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.