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Existence of HPMDs with block size five

✍ Scribed by F. E. Bennett; Y. Chang; J. Yin; H. Zhang

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 194 KB
Volume: 5
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1997)5:4<257::aid-jcd3>3.0.co;2-e

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✦ Synopsis

In this article, it is shown that the necessary condition for the existence of a holey perfect Mendelsohn design (HPMD) with block size 5 and type h n , namely, n ≥ 5 and n(n -1)h 2 ≡ 0 (mod 5), is also sufficient, except possibly for a few cases. The results of this article guarantee the analogous existence results for group divisible designs (GDDs) of group-type h n with block size k = 5 and having index λ = 4. Moreover, some more conclusive results for the existence of (v, 5, 1)-perfect Mendelsohn designs (PMDs) are also mentioned.

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