New lower bounds for t‐coverings. Issue 8 (25th October 2017)

• Record Type: Journal Article
• Authors: Horsley, Daniel; Singh, Rakhi
• Is Part Of: Journal of combinatorial designs. Volume 26:Issue 8(2018:Aug.)
• Page Start: 369
• Page End: 386
• Publication Date: 2017-10-25
• Subjects: Fisher's inequality -- higher incidence matrix -- t‐covering; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21591
• Languages: English
• ISSNs: 1063-8539

Abstract

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