### Abstract

A t-(n,k,λ) design is a k-uniform hypergraph with the property that every set of t vertices is contained in exactly λ of the edges (blocks). A partial t-(n,k,λ) design is a k-uniform hypergraph with the property that every set of t vertices is contained in at most λ edges; or equivalently the intersection of every set of λ+1 blocks contains fewer than t elements. Let us denote by fλ(n,k,t) the maximum size of a partial t-(n,k,λ) design. We determine fλ(n,k,t) as a fundamental problem in design theory and in coding theory. In this paper we provide some new bounds for fλ(n,k,t).

Original language | English |
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Pages (from-to) | 264-275 |

Number of pages | 12 |

Journal | Discrete Mathematics |

Volume | 305 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Dec 6 2005 |

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### Keywords

- Partial block designs

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*305*(1-3), 264-275. https://doi.org/10.1016/j.disc.2005.09.014

**On the size of partial block designs with large blocks.** / Sárközy, A.; Sárközy, Gábor N.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 305, no. 1-3, pp. 264-275. https://doi.org/10.1016/j.disc.2005.09.014

}

TY - JOUR

T1 - On the size of partial block designs with large blocks

AU - Sárközy, A.

AU - Sárközy, Gábor N.

PY - 2005/12/6

Y1 - 2005/12/6

N2 - A t-(n,k,λ) design is a k-uniform hypergraph with the property that every set of t vertices is contained in exactly λ of the edges (blocks). A partial t-(n,k,λ) design is a k-uniform hypergraph with the property that every set of t vertices is contained in at most λ edges; or equivalently the intersection of every set of λ+1 blocks contains fewer than t elements. Let us denote by fλ(n,k,t) the maximum size of a partial t-(n,k,λ) design. We determine fλ(n,k,t) as a fundamental problem in design theory and in coding theory. In this paper we provide some new bounds for fλ(n,k,t).

AB - A t-(n,k,λ) design is a k-uniform hypergraph with the property that every set of t vertices is contained in exactly λ of the edges (blocks). A partial t-(n,k,λ) design is a k-uniform hypergraph with the property that every set of t vertices is contained in at most λ edges; or equivalently the intersection of every set of λ+1 blocks contains fewer than t elements. Let us denote by fλ(n,k,t) the maximum size of a partial t-(n,k,λ) design. We determine fλ(n,k,t) as a fundamental problem in design theory and in coding theory. In this paper we provide some new bounds for fλ(n,k,t).

KW - Partial block designs

UR - http://www.scopus.com/inward/record.url?scp=28544444002&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28544444002&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2005.09.014

DO - 10.1016/j.disc.2005.09.014

M3 - Article

VL - 305

SP - 264

EP - 275

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -