A q–covering design Cq (n, k, r), k ≥ r, is a collection X of (k − 1)–spaces of PG(n − 1, q) such that every (r − 1)–space of PG(n − 1, q) is contained in at least one element of X. Let Cq (n, k, r) denote the minimum number of (k −1)–spaces in a q–covering design Cq (n, k, r). In this paper improved upper bounds on Cq (2n, 3, 2), n ≥ 4, Cq (3n + 8, 4, 2), n ≥ 0, and Cq (2n, 4, 3), n ≥ 4, are presented. The results are achieved by constructing the related q–covering designs.
On q–covering designs / Pavese, Francesco. - In: ELECTRONIC JOURNAL OF COMBINATORICS. - ISSN 1077-8926. - ELETTRONICO. - 27:1(2020). [10.37236/8718]
On q–covering designs
Pavese, Francesco
2020-01-01
Abstract
A q–covering design Cq (n, k, r), k ≥ r, is a collection X of (k − 1)–spaces of PG(n − 1, q) such that every (r − 1)–space of PG(n − 1, q) is contained in at least one element of X. Let Cq (n, k, r) denote the minimum number of (k −1)–spaces in a q–covering design Cq (n, k, r). In this paper improved upper bounds on Cq (2n, 3, 2), n ≥ 4, Cq (3n + 8, 4, 2), n ≥ 0, and Cq (2n, 4, 3), n ≥ 4, are presented. The results are achieved by constructing the related q–covering designs.File in questo prodotto:
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