Pair covering designs with block size 5

R. Julian R. Abel, Ahmed Assaf, Frank E. Bennett, Iliya Bluskov, Malcolm Greig

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

In this article we look at pair covering designs with a block size of 5 and v ≡ 0 (mod 4). The number of blocks in a minimum covering design is known as the covering number C (v, 5, 2). For v ≤ 24, these values are known, and all but v = 8 exceed the Schönheim bound, L (v, 5, 2) = ⌈ v / 5 ⌈ (v - 1) / 4 ⌉ ⌉. However, for all v ≥ 28 with v ≡ 0 (mod 4), it seems probable that C (v, 5, 2) = L (v, 5, 2). We establish this for all but 17 possible exceptional values lying in the range 40 ≤ v ≤ 280.

Original languageEnglish
Pages (from-to)1776-1791
Number of pages16
JournalDiscrete Mathematics
Volume307
Issue number14
DOIs
StatePublished - Jun 28 2007

Keywords

  • Covering design
  • GDD
  • ISBCD
  • PBD
  • Resolvable
  • SBCD

Fingerprint

Dive into the research topics of 'Pair covering designs with block size 5'. Together they form a unique fingerprint.

Cite this