Abstract
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 language | English |
---|---|
Pages (from-to) | 293-299 |
Number of pages | 7 |
Journal | Discrete Mathematics |
Volume | 39 |
Issue number | 3 |
DOIs | |
State | Published - May 1982 |
Externally published | Yes |
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics