Indecomposable Triple Systems without Repeated Blocks

It is proved in this paper that for any given odd integer \(\lambda \geq 1\), 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 \(\lambda(v – 1) \equiv 0 \pmod{2}\) and \(\lambda{v(v – 1)} \equiv 0 \pmod{6}.\)