Group divisible designs with block size 4 and type gum1

被引：12

作者：

Forbes, A. D. ^{[1
]}

Forbes, K. A. ^{[2
]}

机构：

[1] Open Univ, Sch Math & Stat, Walton Hall, Milton Keynes MK7 6AA, Bucks, England

[2] Univ Kingston, Res Business & Innovat, Kingston Upon Thames KT1 2EE, Surrey, England

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2018年 / 26卷 / 11期

关键词：

double group divisible design; group divisible design; GRAPH; HGDDS;

D O I：

10.1002/jcd.21607

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Building upon the work of Wei and Ge (Designs, Codes, and Cryptography 74, 2015), we extend the range of positive integer parameters g, u, and m for which group divisible designs with block size 4 and type gum1 are known to exist. In particular, we show that the necessary conditions for the existence of these designs when m>0 and mg are sufficient in the following cases: , g=2 with one exception, 2(6)5(1), g=10, and g=11.

引用

页码：519 / 539

页数：21

共 47 条

[41] Uniform group divisible designs with block sizes three and n
Chee, YM
Ling, ACH
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[42] Further results on large sets of disjoint group-divisible designs with block size three and type 2n41
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Lei, J
Zhu, L
JOURNAL OF COMBINATORIAL DESIGNS, 2003, 11 (01) : 24 - 35
[43] Construction of group divisible designs and rectangular designs from resolvable and almost resolvable balanced incomplete block designs
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[44] BALANCED TERNARY DESIGNS WITH BLOCK SIZE 4
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[45] Super-simple balanced incomplete block designs with block size 4 and index 6
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[46] Construction of neighbor designs of block size 4 for all values of v ≥ 5 by using the method of addition
Iqbal, I.
Buzdar, P. F.
Ahmed, I.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2018, 47 (10) : 2482 - 2489
[47] Group Divisible Designs with Block Size Four and Type gub1(gu/2)1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g^u b^1 (gu/2)^1$$\end{document}
Anthony D. Forbes
Graphs and Combinatorics, 2020, 36 (6) : 1687 - 1703

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