Abstract
AbstractA large set of Kirkman triple systems of order v, denoted by LKTS(v), is a collection {(X, Bi) : 1 ≤ i ≤ v − 2}, where every (X,Bi) is a KTS(v) and all Bi form a partition of all triples on X. Many researchers have studied the existence of LKTS(v) for a long time. In [13], the author introduced a concept—large set of generalized Kirkman systems (LGKS), which plays an important role in the discussion of LKTS. In this article, we give a new construction for LGKS and obtain some new results of LKTS, that is, there exists an LKTS(6u + 3) for u = qn, where n ≥ 1, q ≡ 7 (mod 12) and q is a prime power. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 202–212, 2008
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