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Existence of directed GDDs with block size five
Author(s) -
Bennett F. E.,
Shalaby Nabil,
Yin Jianxing
Publication year - 1998
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1998)6:6<389::aid-jcd1>3.0.co;2-b
Subject(s) - mathematics , combinatorics , mod , block size , block (permutation group theory) , group (periodic table) , type (biology) , physics , computer science , ecology , computer security , quantum mechanics , key (lock) , biology
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). © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 389–402, 1998