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. Disciplines Physical Sciences and Mathematics Publication Details Seberry, J, Some families of partially balanced incomplete block designs, Combinatorics IX, 952, Lecture Notes in Mathematics, Springer--Verlag, Berlin--Heidelberg--New York, 1982, 378-386. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1009 I C-d~ ;I1J~cO IJ') f~9S-?) ~ $6> e-ra1%.r k4a3 I; SOME FAMILIES OF PARTIALLY BALANCED INCOMPLETE BLOCK DESIGNS 0/-,... I JENNIFER SEBERRY J/~)~) '1r~ i Bhaskar R.ao 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.