Extending symmetric designs

P. J. Cameron*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)


If a symmetric 2-design with parameters (v, k, λ) is extendable, then one of the following holds: v = 4λ + 3, k = 2λ + 1; or v = (λ + 2)(λ2 + 4λ + 2), k = λ2 + 3λ + 1; or v = 111, k = 11, λ = 1; or v = 495, k = 39, λ = 3. In particular, there are at most three sets of extendable symmetric design parameters with any given value of λ. As a consequence, the only twice-extendable symmetric design is the 21-point projective plane.

Original languageEnglish
Pages (from-to)215-220
Number of pages6
JournalJournal of Combinatorial Theory, Series A
Issue number2
Publication statusPublished - 1 Jan 1973


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