Publication Details

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


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.