New constructions for covering designs
| dc.creator | Gordon, Daniel | |
| dc.creator | Kuperberg, Greg | |
| dc.creator | Patashnik, Oren | |
| dc.date | 1995-02-16 | |
| dc.date.accessioned | 2026-07-07T09:15:17Z | |
| dc.date.available | 2026-07-07T09:15:17Z | |
| dc.description | A $(v,k,t)$ {\em covering design}, or {\em covering}, is a family of $k$-subsets, called blocks, chosen from a $v$-set, such that each $t$-subset is contained in at least one of the blocks. The number of blocks is the covering's {\em size}, and the minimum size of such a covering is denoted by $C(v,k,t)$. This paper gives three new methods for constructing good coverings: a greedy algorithm similar to Conway and Sloane's algorithm for lexicographic codes~\cite{lex}, and two methods that synthesize new coverings from preexisting ones. Using these new methods, together with results in the literature, we build tables of upper bounds on $C(v,k,t)$ for $v \leq 32$, $k \leq 16$, and $t \leq 8$.% | |
| dc.identifier | https://arxiv.org/abs/math/9502238 | |
| dc.identifier | http://arxiv.org/abs/math/9502238 | |
| dc.identifier | J. Combin. Des. 4 (1995), no. 4, 269-284 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152967 | |
| dc.subject | Combinatorics | |
| dc.title | New constructions for covering designs | |
| dc.type | text |