Decomposing triples into cyclic designs

Motivated by constructing cyclic simple designs, we consider how to decomposing all the triples of ZvZv into cyclic triple systems. Furthermore, we define a large set of cyclic triple systems to be a decomposition of triples of ZvZv 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 vv with odd v<97v<97 are also given. As an application, the results are used to construct cyclic simple triple systems.