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

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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. Supersimple group divisible designs are useful in constructing other types of supersimple 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)g 2 ≡ 0 (mod 5) with some possible exceptions.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Guangzhou Chen

  2. Department of Mathematics, Taizhou University, Taizhou, 225300, China

    Kejun Chen

  3. School of Mathematical Sciences, Yancheng Teachers University, Yancheng, 224002, China

    Yong Zhang

Authors
  1. Guangzhou Chen
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  2. Kejun Chen
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  3. Yong Zhang
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Correspondence to Guangzhou Chen.

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Chen, G., Chen, K. & Zhang, Y. Super-simple (5, 4)-GDDs of group type g u . Front. Math. China 9, 1001–1018 (2014). https://doi.org/10.1007/s11464-014-0393-3

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  • DOI: https://doi.org/10.1007/s11464-014-0393-3

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