Let (v,u × c,λ)-splitting BIBD denote a (v,u × c,λ)-splitting balanced incomplete block design of order v with block size u × c and index λ. The necessary conditions for the existence of a (v,u × c,λ)-splitting BIBD are v uc, λ(v-1) ≡ 0 0 mod (c(u-1)) and λv(v-1) ≡ 0 mod (c2u(u-1)). In this paper, for 2 λ 9 the necessary conditions for the existence of a (v,3 × 3,λ)-splitting BIBD are also suffcient with one possible exception for (v,λ) = (39,9).
