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Existence of directed GDDs with block size five

✍ Scribed by F. E. Bennett; Nabil Shalaby; Jianxing Yin

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 393 KB
Volume: 6
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1998)6:6<389::aid-jcd1>3.0.co;2-b

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✦ Synopsis

In this article, we construct directed group divisible designs (DGDDs) with block size five, group-type h n , and index unity. The necessary conditions for the existence of such a DGDD are n ≥ 5, (n -1)h ≡ 0 (mod 2) and n(n -1)h 2 ≡ 0 (mod 10). It is shown that these necessary conditions are also sufficient, except possibly for n = 15 where h ≡ 1 or 5 (mod 6) and h ≡ 0 (mod 5), or (n, h) = (15, 9).

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