Geodesic
On \(q\)-covering designs
Francesco Pavese1
1Politecnico di Bari Department of Mechanics Mathematics and Management
The electronic journal of combinatorics, Tome 27 (2020) no. 1
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A $q$-covering design $\mathbb{C}_q (n, k, r)$, $k \ge r$, is a collection $\mathcal{X}$ 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 $\mathcal{X}$ . Let $\mathcal{C}_q(n, k, r)$ denote the minimum number of $(k-1)$-spaces in a $q$-covering design $\mathbb{C}_q (n, k, r)$. In this paper improved upper bounds on $\mathcal{C}_q(2n, 3, 2)$, $n \ge 4$, $\mathcal{C}_q(3n + 8, 4, 2)$, $n \ge 0$, and $\mathcal{C}_q(2n,4,3)$, $n \ge 4$, are presented. The results are achieved by constructing the related $q$-covering designs.
DOI : 10.37236/8718
Classification : 51E20, 05B40, 05B25, 51A05
Mots-clés : \(q\)-covering designs

Francesco Pavese  1

1 Politecnico di Bari Department of Mechanics Mathematics and Management 
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Francesco Pavese. On \(q\)-covering designs. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8718

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