Super-simple group divisible designs with block size 4 and index 9 |
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Authors: | Yong Zhang Kejun Chen |
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Institution: | a Institute of Mathematics, Hebei Normal University, Shijiazhuang, Hebei 050016, China b Department of Mathematics, Yancheng Teachers University, Jiangsu 224002, China |
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Abstract: | A design is said to be super-simple if the intersection of any two blocks has at most two elements. In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple GDDs are useful in constructing super-simple BIBDs. The existence of super-simple (4,λ)‐GDDs has been determined for λ=2-6. In this paper, we investigate the existence of a super-simple (4,9)-GDD of group type gu and show that such a design exists if and only if u≥4, g(u−2)≥18 and u(u−1)g2≡0 (mod 4). |
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Keywords: | Super-simple Group divisible design Balanced incomplete block design |
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