Bhaskar Rao designs over small groups

Authors

William D. Palmer
Jennifer Seberry, University of WollongongFollow

Publication Details

Palmer, WD and Seberry, J, Bhaskar Rao designs over small groups, Ars Combinatoria, 26A, 1988, 125-148.

Abstract

We show that for each of the groups S₃, D₄, Q₄, Z₄ x Z₂ and D₆ the necessary conditions are sufficient for the existence of a generalized Bhaskar Rao design. That is, we show that: (i) a GBRD (v, 3, λ; S3) exists if and only if λ ≡ O (mod 6 ) and λv(v - 1) ≡ O(mod 24); (ii) if G is one of the groups D₄, Q₄, and Z₄ x Z₂, a GBRD (v, 3, λ; G) exists if and only if λ ≡ O(mod 8) and λv(v - 1) ≡ O(mod 6); (iii) a GBRD (v, 3, λ; D₆) exists if and only if λ ≡ O(mod 12). From these designs,families of regular group divisible designs are constructed.