Enumerating Steiner triple systems

Daniel Heinlein*, Patric R.J. Östergård

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Steiner triple systems (STSs) have been classified up to order 19. Earlier estimations of the number of isomorphism classes of STSs of order 21, the smallest open case, are discouraging as for classification, so it is natural to focus on the easier problem of merely counting the isomorphism classes. Computational approaches for counting STSs are here considered and lead to an algorithm that is used to obtain the number of isomorphism classes for order 21: 14,796,207,517,873,771.

Original languageEnglish
Pages (from-to)479-495
Number of pages17
JournalJournal of Combinatorial Designs
Issue number10
Early online date2023
Publication statusPublished - Oct 2023
MoE publication typeA1 Journal article-refereed


  • classification
  • counting
  • regular graph
  • Steiner triple system


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