Super-simple (5, 4)-GDDs of group type gu

doi:10.1007/s11464-014-0393-3

Front. Math. China

2014, Vol. 9

Issue (5) : 1001-1018 https://doi.org/10.1007/s11464-014-0393-3

RESEARCH ARTICLE

Super-simple (5, 4)-GDDs of group type g^u

Guangzhou CHEN¹(

),Kejun CHEN¹,Yong ZHANG¹

1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2. Department of Mathematics, Taizhou University, Taizhou 225300, China
3. School of Mathematical Sciences, Yancheng Teachers University, Yancheng 224002, China

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Abstract

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple group divisible designs are useful in constructing other types of super-simple designs which can be applied to codes and designs. In this article, the existence of a super-simple (5, 4)-GDD of group type g^u is investigated and it is shown that such a design exists if and only if u≥5, g(u - 2)≥12, and u(u - 1)g² ≡ 0 (mod 5) with some possible exceptions.

Keywords Super-simple design group divisible design (GDD) balanced incomplete block design orthogonal array completely reducible

Issue Date: 26 August 2014

Cite this article:

Guangzhou CHEN,Kejun CHEN,Yong ZHANG. Super-simple (5, 4)-GDDs of group type g^u[J]. Front. Math. China, 2014, 9(5): 1001-1018.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0393-3
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I5/1001

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