A tripling construction for overlarge sets of KTS

AbstractAn overlarge set of KTS(v), denoted by OLKTS(v), is a collection {(X∖{x},Bx):x∈X}, where X is a (v+1)-set, each (X∖{x},Bx) is a KTS(v) and {Bx:x∈X} forms a partition of all triples on X. In this paper, we give a tripling construction for overlarge sets of KTS. Our main result is that: If there exists an OLKTS(v) with a special property, then there exists an OLKTS(3v). It is obtained that there exists an OLKTS(3m(2u+1)) for u=22n−1−1 or u=qn, where prime power q≡7 (mod 12) and m≥0,n≥1

Further results on large sets of Kirkman triple systems

AbstractAn LR design is introduced by the second author in his recent paper and it plays a very important role in the construction of LKTS (a large set of disjoint Kirkman triple system). In this paper, we generalize it and introduce a new design RPICS. Some constructions for these two designs are also presented. With the relationship between them and LKTS, we obtain some new LKTSs