On the size of partial block designs with large blocks

András Sárközy, Gábor N. Sárközy

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)264-275
Number of pages12
JournalDiscrete Mathematics
Volume305
Issue number1-3
DOIs
Publication statusPublished - Dec 6 2005

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Keywords

  • Partial block designs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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