Generalized Bhaskar Rao designs

Generalized Bhaskar Rao designs with non-zero elements from an abelian group G are constructed. In particular this paper shows that the necessary conditions are sufficient for the existence of generalized Bhaskar Rao designs with k=3 for the following groups: │G│ is odd, G=Zr2, and G=Zr2 X H where 3+│H│ and r ≥ l. It also constructs generalized Bhaskar Rao designs with v=k, which is equivalent to v rows of a generalized Hadamard matrix of order n where v ≤ n.