Decomposing triples into cyclic designs

AbstractMotivated by constructing cyclic simple designs, we consider how to decomposing all the triples of Zv into cyclic triple systems. Furthermore, we define a large set of cyclic triple systems to be a decomposition of triples of Zv 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