Indecomposable Triple Systems with $\lambda =5$

Abstract

An $\text{NB}[k,\lambda ;v]$ is a $\text{B}[b,\lambda ;v]$ which has no repeated blocks. In this paper we prove that there exists an indecomposable $\text{NB}[3,5;v]$ for $v\ge 7$ and $v\equiv 1\text{ or }3(\mathrm{mod}6)$, with the exception of $v=7$ and $9$, and the possible exception of $v=13,15$.