A new existence proof for large sets of disjoint Steiner triple systems

Abstract: A Steiner triple system of order (briefly STS) consists of a -element set X and a collection of 3-element subsets of X, called blocks, such that every pair of distinct points in X is contained in a unique block. A large set of disjoint STS (briefly LSTS) is a partition of all 3-subsets (triples) of X into STS. In 1983–1984, Lu Jiaxi first proved that there exists an LSTS for any or with six possible exceptions and a definite exception . In 1989, Teirlinck solved the existence of LSTS for the remaining six orders. Since their proof is very complicated, it is much desired to find a simple proof. For this purpose, we give a new proof which is mainly based on the 3-wise balanced designs and partitionable candelabra systems. [Copyright &y& Elsevier]