Abstract
In this article we look at pair covering designs with a block size of 5 and v ≡ 0 (mod 4). The number of blocks in a minimum covering design is known as the covering number C (v, 5, 2). For v ≤ 24, these values are known, and all but v = 8 exceed the Schönheim bound, L (v, 5, 2) = ⌈ v / 5 ⌈ (v - 1) / 4 ⌉ ⌉. However, for all v ≥ 28 with v ≡ 0 (mod 4), it seems probable that C (v, 5, 2) = L (v, 5, 2). We establish this for all but 17 possible exceptional values lying in the range 40 ≤ v ≤ 280.
Original language | English |
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Pages (from-to) | 1776-1791 |
Number of pages | 16 |
Journal | Discrete Mathematics |
Volume | 307 |
Issue number | 14 |
DOIs | |
State | Published - Jun 28 2007 |
Keywords
- Covering design
- GDD
- ISBCD
- PBD
- Resolvable
- SBCD