Decomposing triples into cyclic designs. (English) Zbl 1231.05028
Summary: Motivated by constructing cyclic simple designs, we consider how to decomposing all the triples of \(\mathbb Z_v\) into cyclic triple systems. Furthermore, we define a large set of cyclic triple systems to be a decomposition of triples of \(\mathbb Z_v\) 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.
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