Pair covering designs with block size 5

R. Julian R. Abel; Ahmed Assaf; Frank E. Bennett; Iliya Bluskov; Malcolm Greig

doi:10.1016/j.disc.2006.09.026

Pair covering designs with block size 5

R. Julian R. Abel, Ahmed Assaf, Frank E. Bennett, Iliya Bluskov, Malcolm Greig

Mathematics

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11 Scopus citations

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
Pages (from-to)	1776-1791
Number of pages	16
Journal	Discrete Mathematics
Volume	307
Issue number	14
DOIs	https://doi.org/10.1016/j.disc.2006.09.026
State	Published - Jun 28 2007

Keywords

Covering design
GDD
ISBCD
PBD
Resolvable
SBCD

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10.1016/j.disc.2006.09.026

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title = "Pair covering designs with block size 5",

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 Sch{\"o}nheim 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.",

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T1 - Pair covering designs with block size 5

AU - R. Abel, R. Julian

AU - Assaf, Ahmed

AU - Bennett, Frank E.

AU - Bluskov, Iliya

AU - Greig, Malcolm

PY - 2007/6/28

Y1 - 2007/6/28

N2 - 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.

AB - 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.

KW - Covering design

KW - GDD

KW - ISBCD

KW - PBD

KW - Resolvable

KW - SBCD

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DO - 10.1016/j.disc.2006.09.026

M3 - Article

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SP - 1776

EP - 1791

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 14

ER -

Pair covering designs with block size 5

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Keywords

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