Generalized Bhaskar Rao designs with two association classes

GENERALIZED BHASKAR RAO DESIGNS WITH TWO ASSOCIATION CLASSES William D. PALMER Department of Pure Mathematics The University of Sydney and Department of Mathematics Sydney Institute of Education In previous work generalized Bhaskar Rao designs whose underlying design is a b~lanced incomplete block design have been considered. In the first section of this paper generalized Bhaskar Rao designs (with 2 association classes) whose underlying design is a group divisible design are defin~d. Some methods for the construction of these designs are developed in the second section. It is shown that the necessary conditions: A 0 (mod g) v 0 (mod 2 ) v ~ 6 Av(v-2) 0 (mod 3 ) are sufficient for the exi~tence of a GBRD(v,3,A,2:EA(g}) where EA(g) is an elementary abelian group of order g. Finally. the design GBRD(v,b,r,3,Al = O,A2 = A.2;EA(g) is used to construct a group divisible design with v/2 groups each of siz~ 2g and with the-parameters v ... = v g, b ... = b g, r ... = r,k'" = 3, AlII' = 0, A 2 * A/g. °