منابع مشابه
Some Block Designs Constructed from Resolvable Designs
LetD be a resolvable 2−(v, k, λ) design, andD′ be a 2−(v′, k′, λ′) design, such that v′ = v k . Further, let r and r′ be replication numbers of a point in D and D′, respectively. Shrikhande and Raghavarao proved that then there exists a 2 − (v′′, k′′, λ′′) design D′′, such that v′′ = v, k′′ = kk′ and λ′′ = r′λ + (r − λ)λ′. If D′ is resolvable, then D′′ is also resolvable. Applying this result, ...
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In his book [I 1, Marshall Hall gives a table of balanced incomplete block designs with from 3 to 15 replications. It is mentioned there that a solution is unknown as to whether or not there exists a symmetric block design with parameters (v, k, h) = (36, 15, 6) (number 104 in the table). It is the purpose of this paper to show that such a design can in fact be constructed quite simply and to s...
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The design of experiments involving more than one blocking factor and quantitative explanatory variables is discussed, the focus being on two key aspects of blocked response surface designs: optimality and orthogonality. First, conditions for orthogonally blocked experiments are derived. Next, an algorithmic approach to computeD-optimal designs is presented. Finally, the relationships between d...
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Some new series of block designs with nested rows and columns have been constructed with some examples mainly from a combinatorial point of view. Two of the series are balanced (ternary), the others are partially balanced, based on rectangular and triangular association schemes.
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Some techniques are developed for constructing non-isomorphic solutions of symmetric (4t + 3,2t + 1, t) designs for suitable values of t and for (4t + 2, 8t + 2,4t + 1,2t + 1,2t) and (4t + 4, St + 6,4t + 3,2t + 2,2t + 1) designs. As an application, some non-isomorphic solutions of (19,9,4), (10,18, 9, 5, 4), and (12, 22, 11, 6, 5) designs are obtained. In [l] some other techniques were given fo...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1989
ISSN: 0012-365X
DOI: 10.1016/0012-365x(89)90356-7