Geodesic
5-sparse Steiner triple systems of order \(n\) exist for almost all admissible \(n\)
The electronic journal of combinatorics, Tome 12 (2005)

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Zbl EuDML
Steiner triple systems are known to exist for orders $n \equiv 1,3$ 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.
DOI : 10.37236/1965
Classification : 05B07 
Adam Wolfe. 5-sparse Steiner triple systems of order \(n\) exist for almost all admissible \(n\). The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1965
@article{10_37236_1965,
     author = {Adam Wolfe},
     title = {5-sparse {Steiner} triple systems of order \(n\) exist for almost all admissible \(n\)},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1965},
     zbl = {1079.05013},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1965/}
}
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