Large sets of Kirkman triple systems with order qn+2

The existence of Large sets of Kirkman Triple Systems (LKTS) is an old problem in combinatorics. Known results are very limited, and a lot of them are based on the works of Denniston (1974, 1979) [2,3,5,4]. The only known recursive constructions are a tripling construction by Denniston (1979) [5] and a product construction by Lei (2002). Both construct an LICTS(uv) on the basis of an LICTS(v). In this paper, we describe a construction of LKTS(q(n) + 2) from LKTS(q + 2), where q is a prime power of the form 6t + 1. We could construct previous unknown LKTS(v) by this result, the smallest among them have v = 171, 345, 363. (C) 2016 Elsevier B.V. All rights reserved.