Projective covering designs
A (2, k, v) covering design is a pair (X, F) such that X is a v-element set and F is a family of k-element subsets, called blocks, of X with the property that every pair of distinct elements of X is contained in at least one block. Let C(2, k, v) denote the minimum number of blocks in a (2, k, v) co...
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| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/95779 http://hdl.handle.net/10220/9828 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | A (2, k, v) covering design is a pair (X, F) such that X is a v-element set and F is a family of k-element subsets, called blocks, of X with the property that every pair of distinct elements of X is contained in at least one block. Let C(2, k, v) denote the minimum number of blocks in a (2, k, v) covering design. We construct in this paper a class of (2, k, v) covering designs using number theoretic means, and determine completely the functions C(2,6,6n · 28) for all n ≥ 0, and C(2,6,6n · 28 − 5) for all n ≥ 1. Our covering designs have interesting combinatorial properties. |
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