Pair covering designs with block size 5

被引：6

作者：

Abel, R. Julian R. ^{[1
]}

Assaf, Ahmed

Bennett, Frank E.

Bluskov, Iliya

Greig, Malcolm

机构：

[1] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[2] Cent Michigan Univ, Dept Math, Mt Pleasant, MI 48859 USA

[3] Mt St Vincent Univ, Dept Math, Halifax, NS B3M 2J6, Canada

[4] Univ No British Columbia, Dept Math & Comp Sci, Prince George, BC V2N 4Z9, Canada

[5] Greig Consulting, N Vancouver, BC V7L 4R3, Canada

来源：

DISCRETE MATHEMATICS | 2007年 / 307卷 / 14期

关键词：

covering design; SBCD; ISBCD; GDD; PBD; resolvable;

D O I：

10.1016/j.disc.2006.09.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Schonheim 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. (C) 2006 Elsevier B.V. All rights reserved.

引用

页码：1776 / 1791

页数：16

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