Group divisible designs, GBRDSDS and generalized weighing matrices

Authors

Dinesh G. Sarvate
Jennifer Seberry, University of WollongongFollow

Publication Details

Dinesh Sarvate and Jennifer Seberry, Group divisible designs, GBRDSDS and generalized weighing matrices, Utilitas Mathematica, 54, (1998), 157-174.

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 PDB(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).