A completion of the spectrum for large sets of disjoint transitive triple systems (Q1193578)

A transitive triple system on \(v\) points \(\text{TTS}(v)\), is a partition of the arcs of the complete symmetric graph on \(v\) vertices into transitive triples. (Necessarily \(v \equiv 0, 1 \pmod 3\).) A large set of \(\text{TTS}(v)\) is a partition of all \(v(v-1)(v-2)\) transitive triples on \(v\) points into \(3(v-2) \text{TTS}(v)\). The authors provide a construction of a large set of \(\text{TTS}(2^ n+2)\) for all \(n \geq 0\) which combined with earlier work on the problem suffices to show that a large set of \(\text{TTS}(v)\) exists for all \(v \equiv 0, 1 \pmod 3\).