Balanced nested designs and balanced arrays
نویسندگان
چکیده
منابع مشابه
Balanced nested designs and balanced arrays
Balanced nested designs are closely related to other combinatorial structures such as balanced arrays and balanced n-ary designs. In particular, the existence of symmetric balanced nested designs is equivalent to the existence of some balanced arrays. In this paper, various constructions for symmetric balanced nested designs are provided. They are used to determine the spectrum of symmetric bal...
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We introduce here two types of balanced nested designs (BND), which are called symmetric and pair-sum BNDs. In this paper, we give a construction for pair-sum BNDs of BIBDs from nested BIBDs and perpendicular arrays. We also give some direct constructions for pair-sum BNDs of BIBDs, based on the result obtained by Wilson (1972). By use of these constructions, we show some constructions for regu...
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An (r,λ)-design with mutually balanced nested subdesigns ( for brevity, (r,λ)-design with MBN ) is introduced firstly in this paper. It is shown that an (r,λ)design with MBN is equivalent to a balanced array of strength 2 with s symbols. By the use of a nested design and an orthogonal array, a construction of an (r,λ)design with MBN is given. A direct construction of such an (r,λ)-design, based...
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Balanced nesting is the most usual form of nesting and originates, when used singly or with crossing of such sub-models, orthogonal models. In balanced nesting we are forced to divide repeatedly the plots and we have few degrees of freedom for the first levels. If we apply stair nesting we will have plots all of the same size rendering the designs easier to apply. The stair nested designs are a...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00356-4