Cyclic, Simple, and Indecomposable Three-fold Triple Systems

Abstract

In 2000, Rees and Shalaby constructed simple indecomposable two-fold cyclic triple systems for all $v\equiv 0,1,3,4,7,\text{ and }9(\mathrm{mod}12)$ where $v=4$ or $v\ge 12$, using Skolem-type sequences.
We construct, using Skolem-type sequences, three-fold triple systems having the properties of being cyclic, simple, and indecomposable for all admissible orders $v$, with some possible exceptions for $v=9$ and $v=24c+57$, where $c\ge 2$ is a constant.