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Full-Text Articles in Physical Sciences and Mathematics
Generalized Bhaskar Rao Designs With Block Size 3 Over Finite Abelian Groups, G. Ge, M. Grieg, Jennifer Seberry, R. Seberry
Generalized Bhaskar Rao Designs With Block Size 3 Over Finite Abelian Groups, G. Ge, M. Grieg, Jennifer Seberry, R. Seberry
Professor Jennifer Seberry
We show that if G is a finite Abelian group and the block size is 3, then the necessary conditions for the existence of a (v; 3; λ;G) GBRD are sufficient. These necessary conditions include the usual necessary conditions for the existence of the associated (v; 3; λ) BIBD plus λ ≡ 0 (mod |G|), plus some extra conditions when |G| is even, namely that the number of blocks be divisible by 4 and, if v = 3 and the Sylow 2-subgroup of G is cyclic, then also λ ≡ 0 (mod 2|G|).
Generalized Bhaskar Rao Designs With Block Size 4 Signed Over Elementary Abelian Groups , G. Ge, M. Greig, Jennifer Seberry
Generalized Bhaskar Rao Designs With Block Size 4 Signed Over Elementary Abelian Groups , G. Ge, M. Greig, Jennifer Seberry
Professor Jennifer Seberry
de Launey and Seberry have looked at the existence of Generalized Bhaskar Rao designs with block size 4 signed over elementary Abelian groups and shown that the necessary conditions for the existence of a (v, 4, λ; EA(g)) GBRD are sufficient for λ > g with 70 possible exceptions. This article extends that work by reducing those possible exceptions to just a (9,4,18h; EA(9h)) GBRD, where gcd(6, h) = 1, and shows that for λ = g the necessary conditions are sufficient for v > 46.