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) GW(21;9;Z3). The GDD obtained are not found in W.H. Clatworthy, Tables of TwoAssociateClass, Partially Balanced Designs, NBS, US Department of Commerce, 1971.