Quadruple systems containing AG(3,2)

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A quadruple system of order v, denoted QS(v) is an ordered pair (X, Q) where X is a set of cardinality v and Q is a set of 4-subsets of X called blocks, with the property that every 3-subset of X is contained in a unique block. The points and planes of the affine geometry AG(3, 2) form a QS(8). We prove that a QS(v) containing a proper subsystem isomorphic to AG(3, 2) exists if and only if v≥16 and v≡2 or 4 (mod 6).

Original languageEnglish
Pages (from-to)293-299
Number of pages7
JournalDiscrete Mathematics
Issue number3
StatePublished - May 1982
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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