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Abstract: We give the first known examples of 6-sparse Steiner triple systems by constructing 29 such systems in the residue class 7 modulo 12, with orders ranging from 139 to 4447. We then present a recursive construction which establishes the existence of 6-sparse systems for an infinite set of orders. Observations are also made concerning existing construction methods for perfect Steiner triple systems, and we give a further example of such a system. This has order 135,859 and is only the fourteenth known. Finally, we present a uniform Steiner triple system of order 180,907. [Copyright &y& Elsevier]

Abstract: In [Z. Füredi, Turán type problems, in: Surveys in Combinatorics, Guildford, 1991, in: London Math. Soc. Lecture Note Ser., vol. 166, Cambridge Univ. Press, Cambridge, 1991, pp. 253–300, MR1161467 (93d:05072)], Füredi raised a conjecture about the maximum size of L-intersecting families. In this note, we address a variant of this conjecture. In particular, we show that for any Steiner triple system on , there exist a family of k-sets on with and such that for every the family is isomorphic to . [Copyright &y& Elsevier]

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]