Some new large sets of KTS\((v)\) (Q2761070)

A Kirkman triple system \(\text{KTS}(v)\) is a Steiner triple system \((X,\mathcal A)\), where \(\mathcal A\) can be partitioned into such disjoint classes that each \(x\in X\) is contained in exactly one triple of each of the classes. A collection of \(v-2\) pairwise disjoint \(\text{KTS}(v)\) is called a large set of \(\text{KTS}(v)\). A necessary condition for a \(\text{LKTS}(v)\) to exist is \(v\equiv 3\pmod 6\). The author constructs \(\text{LKTS}(v)\) for \(v\in \{201,369\}\) and for \(v=3^n\cdot 67\), \(n\geq 1\). These results are corollaries of more technical statements that use certain partitions of \(\text{GF}(q)\), \(q \equiv 1\pmod 6\).