Decomposing triples into cyclic designs

Motivated by constructing cyclic simple designs, we consider how to decomposing all the triples of Z v into cyclic triple systems. Furthermore, we define a large set of cyclic triple systems to be a decomposition of triples of Z v into indecomposable cyclic designs. Constructions of decompositions and large sets are given. Some infinite classes of decompositions and large sets are obtained. Large sets of small v with odd v < 97 are also given. As an application, the results are used to construct cyclic simple triple systems.