Another construction for large sets of Kirkman triple systems

Abstract

A large set of Kirkman triple systems of order v, denoted by LKTS(v), is a collection $\{(X, \mathcal {B}_i) : 1 \leq i \leq v - 2\}$, where every $(X, \mathcal {B}_i)$ is a KTS(v) and all $\mathcal {B}_i$ form a partition of all triples on X. In this article, we give a new construction for LKTS(6v + 3) via OLKTS(2v + 1) with a special property and obtain new results for LKTS, that is there exists an LKTS(3v) for $v = \prod_{i=1}^{p}(2q_i^{r_i}+1)\prod_{j=1}^{q}(4^{s_j}-1)$, where p, q ≥ 0, r _i , s _j ≥ 1, q _i is a prime power and $q_i \equiv 7$ mod 12.