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5-sparse Steiner triple systems of order $$n$$ exist for almost all admissible $$n$$. (English) Zbl 1079.05013
Summary: Steiner triple systems are known to exist for orders $$n = 1,3$$ mod 6, the admissible orders. There are many known constructions for infinite classes of Steiner triple systems. However, Steiner triple systems that lack prescribed configurations are harder to find. This paper gives a proof that the spectrum of orders of 5-sparse Steiner triple systems has arithmetic density 1 as compared to the admissible orders.

##### MSC:
 05B07 Triple systems
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