Generalized Bhaskar Rao Designs with Block Size 3 over Finite Abelian Groups

G. Ge, Zhejiang University, China
M. Grieg, Greig Consulting, North Vancouver, B.C., Canada
J. Seberry, University of Wollongong
R. Seberry, Turramurra, Australia

Article comments

This article was originally published as Ge, G, Grieg, M, Seberry, J, & Seberry, R, Generalized Bhaskar Rao Designs with Block Size 3 over Finite Abelian Groups, Graphs and Combinatorics, 23(3), 2007, 271-290. The original publication is available at www.springerlink.com.

Abstract

We show that if G is a finite Abelian group and the block size is 3, then the necessary conditions for the existence of a (v; 3; λ;G) GBRD are sufficient. These necessary conditions include the usual necessary conditions for the existence of the associated (v; 3; λ) BIBD plus λ ≡ 0 (mod |G|), plus some extra conditions when |G| is even, namely that the number of blocks be divisible by 4 and, if v = 3 and the Sylow 2-subgroup of G is cyclic, then also λ ≡ 0 (mod 2|G|).