New lower bounds for t‐coverings. Issue 8 (25th October 2017) - Horsley, Daniel; Singh, Rakhi
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.