New lower bounds for t-coverings

Daniel Horsley, Rakhi Singh

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

Fisher proved in 1940 that any 2- (v,k,λ) design with (Formula presented.) has at least v blocks. In 1975, Ray-Chaudhuri and Wilson generalized this result by showing that every t- (Formula presented.) design with (Formula presented.) has at least (Formula presented.) blocks. By combining methods used by Bose and Wilson in proofs of these results, we obtain new lower bounds on the size of t- (Formula presented.) coverings. Our results generalize lower bounds on the size of 2- (Formula presented.) coverings recently obtained by the first author.

Original languageEnglish
Pages (from-to)369-386
Number of pages18
JournalJournal of Combinatorial Designs
Volume26
Issue number8
DOIs
Publication statusPublished - 1 Aug 2018

Keywords

  • Fisher’s inequality
  • higher incidence matrix
  • t-covering

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