#### Abstract

We give new constructions for regular group divisible designs, pairwise balanced designs, generalized Bhaskar Rao supplementary difference sets and generalized weighing matrices. In particular if p is a prime power and q divides p – 1 we show the following exist:

(i) GDD(2(p2 +p+ 1), 2(p2 +p+ 1), rp2, 2p2, λ1 = p2λ, λ2 = (p2 —p)r, m = p2 + p+ 1, n = 2), r = 1,2;

(ii) GDD(q(p+ 1), q(p+ 1), p(q – 1), p(q –1), λ1 = (q – 1)(q – 2), λ2 = (p– 1)(q – 1)2/q, m = q, n = p+1);

(iii) PBD(21, 10; K), K = {3, 6, 7} and PBD(78, 38; K), K = {6, 9, 45};

(iv) GW(vk, k2; EA(k)) whenever a (v, k, λ)-difference set exists and k is a prime power;

(v) PBIBD(vk2, vk2, k2, k2; λ1 = 0, λ2 = λ, λ3 = k) whenever a (v, k, λ)-difference set exists and k is a prime power;

(vi) we give a GW(21; 9; Z3).

The GDD obtained are not found in W.H. Clatworthy, “Tables of Two-Associate-Class, Partially Balanced Designs”, NBS, US Department of Commerce, 1971.

## Publication Details

This article was originally published as Sarvate, DG and Seberry, J, Group Divisible Designs, GBRSDS And Generalized Weighing Matrices, Utilitas Mathematica, 54, 1998, 157-174.