Indecomposable Triple Systems with $\lambda =6$

Abstract

A triple system $B[3,\lambda ;v]$ is indecomposable if it is not the union of two triple systems $B[3,{\lambda }_1;v]$ and $B[3,{\lambda }_2;v]$ with $\lambda ={\lambda }_1+{\lambda }_2$. We prove that indecomposable triple systems with $\lambda =6$ exist for $v=8,14$ and for all $v\ge 17$.