Indecomposable Triple Systems without Repeated Blocks

Abstract

It is proved in this paper that for any given odd integer $\lambda \ge 1$, there exists an integer $v_0=v_0(\lambda )$, such that for $v>v_0$, the necessary and sufficient conditions for the existence of an indecomposable triple system $B(3,\lambda ;v)$ without repeated blocks are $\lambda (v–1)\equiv 0(\mathrm{mod}2)$ and $\lambda v(v–1)\equiv 0(\mathrm{mod}6).$