Some families of partially balanced incomplete block designs

Bhaskar Rao designs with elements from abelian groups are defined and it is shown how such designs can be used to obtain group divisible partially balanced incomplete block designs with group size g, where g is the order of the abelian group. This paper studies the group Z3 and shows, using recursive constructions given here, that the necessary conditions are sufficient for the existence of generalized Bhaskar Rao designs. These designs are then used to obtain families of partially balanced designs.