FURTHER RESULTS ON THE EXISTENCE OF SUPER-SIMPLE PAIRWISE BALANCED DESIGNS WITH BLOCK SIZES 3 AND 4

Chen Guangzhou; Guo Yue; Zhang Yong

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FURTHER RESULTS ON THE EXISTENCE OF SUPER-SIMPLE PAIRWISE BALANCED DESIGNS WITH BLOCK SIZES 3 AND 4

机译：进一步导致存在具有块尺寸3和4的超简单成对平衡设计

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In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple pairwise balanced designs are useful in constructing other types of super-simple designs which can be applied to codes and designs. In this paper, the super-simple pairwise balanced designs with block sizes 3 and 4 are investigated and it is proved that the necessary conditions for the existence of a super-simple (v; {3; 4}; lambda)-PBD for lambda = 7; 9 and lambda = 2 k, k >= 1, are sufficient with seven possible exceptions. In the end, several optical orthogonal codes and superimposed codes are given.

机译：在实验的统计规划中，超简单的设计是提供样品的最大交叉点尽可能小。超简单的成对平衡设计可用于构建其他类型的超简单设计，该设计可以应用于代码和设计。在本文中，研究了具有块尺寸3和4的超简单的成对平衡设计，证明存在超简单（v; {3; 4}; lambda）-pbd的必要条件 = 7; 9和Lambda = 2 k，k> = 1，足以有七种可能的例外情况。在最后，给出了几种光学正交码和叠加码。

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来源
《Advances in mathematics of communications》 |2018年第2期|共12页
作者
Chen Guangzhou; Guo Yue; Zhang Yong;
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作者单位

Henan Normal Univ Sch Math &

Informat Sci Xinxiang 453007 Peoples R China;

Henan Normal Univ Sch Math &

Informat Sci Xinxiang 453007 Peoples R China;

Yancheng Teachers Univ Sch Math &

Stat Yancheng 224002 Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Super-simple designs; pairwise balanced designs; balanced incomplete block designs; group divisible designs; optical orthogonal code;

机译：超简单的设计;成对平衡设计;平衡不完整的块设计;组可分层设计;光学正交码;

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专利

1. FURTHER RESULTS ON THE EXISTENCE OF SUPER-SIMPLE PAIRWISE BALANCED DESIGNS WITH BLOCK SIZES 3 AND 4 [J] . Chen Guangzhou, Guo Yue, Zhang Yong Advances in mathematics of communications . 2018,第2期

机译：进一步导致存在具有块尺寸3和4的超简单成对平衡设计
2. Super-simple balanced incomplete block designs with block size 5 and index 3 [J] . Chen K., Chen G., Li W., Discrete Applied Mathematics . 2013,第16a17期

机译：具有块大小5和索引3的超简单平衡不完整块设计
3. Super-Simple Resolvable Balanced Incomplete Block Designs with Block Size 4 and Index 4 [J] . Liu H., Wang L. Graphs and combinatorics . 2013,第5期

机译：具有块大小4和索引4的超简单可解析平衡不完整块设计
4. Construction of amicably resolvable Pairwise Balanced Design from row-regular Williamson type matrices [C] . M. K. Singh, Pinky Pandey 2016 3rd International Conference on Recent Advances in Information Technology . 2016

机译：从行规则的Williamson型矩阵构造友善可解决的成对平衡设计
5. Pairwise balanced designs and related codes. [D] . Ling, Chi H. A. 1997

机译：成对平衡设计和相关代码。
6. Balanced incomplete block designs in biological assay illustrated by the assay of gastrin using a youden square [O] . D. Colquhoun 1963

机译：生物学测定中平衡的不完全嵌段设计通过使用尤登广场的胃泌素测定来说明
7. Further results on the existence of super-simple pairwise balanced designs with block sizes 3 and 4 [O] . Guangzhou Chen, Yue Guo, Yong Zhang 2018

机译：进一步导致存在具有块尺寸3和4的超简单成对平衡设计

FURTHER RESULTS ON THE EXISTENCE OF SUPER-SIMPLE PAIRWISE BALANCED DESIGNS WITH BLOCK SIZES 3 AND 4

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