Super-simple balanced incomplete block designs with block size 5 and index 3
نویسندگان
چکیده
منابع مشابه
Super-simple balanced incomplete block designs with block size 5 and index 3
In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in constructing codes and designs such as superimposed codes and perfect hash families. The existence of super-simple (v, 4, λ)BIBDs have been determined for λ = 2, 3, 4, 5, 6. In this paper, we investigate the existence...
متن کاملSuper-simple balanced incomplete block designs with block size 4 and index 5
In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in other constructions, such as superimposed codes and perfect hash families etc. The existence of super-simple (v, 4, λ)-BIBDs have been determined for λ = 2, 3, 4 and 6. When λ = 5, the necessary conditions of such a d...
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The necessary conditions for the existence of a super-simple resolvable balanced incomplete block design on v points with block size k = 4 and index λ = 2, are that v ≥ 16 and v ≡ 4 (mod 12). These conditions are shown to be sufficient. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 341–356, 2007
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The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that: λ(v − 1) ≡ 0 mod (k − 1) λv(v − 1) ≡ 0 mod k(k − 1) Earlier work has studied k = 9 with λ ∈ {1, 2, 3, 4, 6, 8, 9, 12}. In this article we show that the necessary conditions are sufficient for λ = 9 and every other λ not previously studied.
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In this paper, we investigate the existence of a super-simple (4, 5)-GDD of type gu and show that such a design exists if and only if u ≥ 4, g(u − 2) ≥ 10, g(u − 1) ≡ 0 (mod 3) and u(u− 1)g2 ≡ 0 (mod 12). © 2009 Elsevier B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.05.007