English

Steiner triple systems without parallel classes

Combinatorics 2020-07-28 v3

Abstract

We construct Steiner triple systems without parallel classes for an infinite number of orders congruent to 3(mod6)3 \pmod{6}. The only previously known examples have order 1515 or 2121.

Keywords

Cite

@article{arxiv.1407.5766,
  title  = {Steiner triple systems without parallel classes},
  author = {Darryn Bryant and Daniel Horsley},
  journal= {arXiv preprint arXiv:1407.5766},
  year   = {2020}
}

Comments

5 pages, 0 figures. This version fixes a minor error in the journal version of the paper where we had neglected to say that two sum-zero triples must be removed before the additional triples in $\mathcal{B}^\infty \cup \mathcal{B}^*$ are added to create the Steiner triple system

R2 v1 2026-06-22T05:09:36.986Z