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2000000 Steiner triple systems of order 19. (English) Zbl 0564.05011

A Steiner triple system of order v (denoted STS(v)) is a pair (X,B), where X is a set of v elements and B is a set of 3-subsets of X such that every pair of elements of X occurs in a unique block (element of B). If N(v) is the number of nonisomorphic STS(v), then it is known that \(N(1)=N(3)=N(7)=N(9)=1\), \(N(13)=2\), \(N(15)=80\). Results concerning N(19) include enumerations of particular classes of STS(19). In this paper the authors prove that there exist more than 2.000.000 STS(19).
Reviewer: M. Gionfriddo

MSC:

05B07 Triple systems
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