INDECOMPOSABLE TRIPLE-SYSTEMS WITHOUT REPEATED BLOCKS

It is proved in this paper that for any given odd integer lambda greater-than-or-equal-to 1, there exists an integer v0 = v0 (lambda), such that for v > v0, the necessary and sufficient conditions for die existence of an indecomposable triple system B(3, lambda; v) without repeated blocks are, lambda(v - 1) = 0 (mod 2) and lambda-v(v - 1) = 0 (mod 6).