Some infinite families of large sets of Kirkman triple systems

Abstract

Abstract A large set of Kirkman triple systems of order v , denoted by LKTS ( v ), is a collection {( X , B i ) : 1 ≤ i ≤ v − 2}, where every ( X , B i ) is a KTS ( v ) and all B i 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 (6 u + 3) for u = q n , where n ≥ 1, q ≡ 7 (mod 12) and q is a prime power. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 202–212, 2008