### Abstract

A Steiner quadruple system SQS(v) of order v is a family [formula omitted] of 4-element subsets of a v-element set V such that each 3-element subset of V is contained in precisely one B [formula omitted]. We prove that if T [formula omitted] B ≠ ø for all B [formula omitted] (i.e., if T is a transversal), then |T| ≥ v/2, and if T is a transversal of cardinality exactly v/2, then V \ T is a transversal as well (i.e., T is a blocking set). Also, in respect of the so-called ‘doubling construction’ that produces SQS(2v) from two copies of SQS(v), we give a necessary and sufficient condition for this operation to yield a Steiner quadruple system with blocking sets.

Original language | English |
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Pages (from-to) | 77-86 |

Number of pages | 10 |

Journal | Combinatorics, Probability and Computing |

Volume | 3 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1994 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Combinatorics, Probability and Computing*,

*3*(1), 77-86. https://doi.org/10.1017/S0963548300000997