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Pair covering designs with block size 5 |
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| Authors: | R. Julian R. Abel Iliya Bluskov Malcolm Greig |
| Affiliation: | a School of Mathematics and Statistics, University of New South Wales, Sydney N.S.W. 2052, Australia b Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USA c Department of Mathematics, Mount Saint Vincent University, Halifax, NS, Canada B3M 2J6 d Department of Mathematics and Computer Science, University of Northern British Columbia, Prince George, BC, Canada V2N 4Z9 e Greig Consulting, 317-130 East 11th Street, North Vancouver, BC, Canada V7L 4R3 |
| Abstract: | In this article we look at pair covering designs with a block size of 5 and  . 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  , 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. |
| Keywords: | Covering design SBCD ISBCD GDD PBD Resolvable |
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