There is no McLaughlin geometry

Patric R.J. Östergård, Leonard H. Soicher

Research output: Contribution to journalArticleScientificpeer-review


We determine that there is no partial geometry G with parameters (s,t,α)=(4,27,2). The existence of such a geometry has been a challenging open problem of interest to researchers for almost 40 years. The particular interest in G is due to the fact that it would have the exceptional McLaughlin graph as its point graph. Our proof makes extensive use of symmetry and high-performance distributed computing, and details of our techniques and checks are provided. One outcome of our work is to show that a pseudogeometric strongly regular graph achieving equality in the Krein bound need not be the point graph of any partial geometry.

Original languageEnglish
Pages (from-to)27-41
Number of pages15
JournalJournal of Combinatorial Theory. Series A
Publication statusPublished - 1 Apr 2018
MoE publication typeA1 Journal article-refereed


  • Backtrack search
  • Krein bound
  • McLaughlin geometry
  • McLaughlin graph
  • Partial geometry
  • Pseudogeometric graph


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