A Note on Steiner Triple Systems

摘要

Given a set E of e elements, an arrangement of the elements of E in triples is denoted by Steiner triple system in such a way that each pair of elements is contained in exactly one triple. A necessary and sufficient condition for the existence of a Steiner triple system is that e = 1 or 3 (mod 6). The number of the triples in such system is 1/6 e(e-1). A new method of construction of Steiner triple systems in the case e = 6t + 1 is given. (Author)