Construction of some balanced incomplete block designs with nested rows and columns
Construction of some balanced incomplete block designs with nested rows and columns
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构建一些具有嵌套行和列的平衡不完全块设计
DOI：
10.1093/biomet/76.2.399
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发表时间：
1989
期刊：
影响因子：
2.7
通讯作者：
P. Sreenath
中科院分区：
文献类型：
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作者：
P. Sreenath
PAr(i,j) + qAc(ij) -As(j,j) = A, (1-) 其中 A 是一个常数整数，与所选的对 (i,j) 无关，满足关系 A(v -1) = r(p 1)(q -1)； Ar(ij)、Ac(ij) 和 A,(i,j) 分别表示集合内的行数、集合内的列数以及该对同时出现的集合。这些方差平衡二元设计由 Singh & Dey (1979) 介绍和讨论，参数为 v、b、r、p、q 和 A，缩写为 BIBRC (v、b、r、p、q、A)。请注意，(1 1) 是条件 (4-3) 的替代版本。 Agarwal & Prasad (1982, 1983) 和 Cheng (1986) 给出了构建这些设计的进一步方法。 Cheng（1986）在这些设计中考虑了 k = v 的情况，并将其称为带有参数 v、b、r、p、q 和 A 的嵌套行和列的平衡完全块设计，缩写为 BCBRC（v、b、r、p、q、A）。他同样使用了这个条件
PAr(i,j) + qAc(ij) -As(j,j) = A, (1-) where A, a constant integer, independent of the pair (i,j) chosen, satisfies the relationship A(v -1) = r(p 1)(q -1); Ar(ij), Ac(ij) and A,(i,j) denote, respectively, the numbers of rows within sets, columns within sets and sets in which the pair occurs together. These variance balanced binary designs, introduced and discussed by Singh & Dey (1979), with parameters v, b, r, p, q and A, are abbreviated as BIBRC (v, b, r, p, q, A). Note that (1 1) is an alternative version of their condition (4-3). Agarwal & Prasad (1982, 1983) and Cheng (1986) gave further methods of construction of these designs. Cheng (1986) considered the case of k = v in these designs and called them balanced complete block designs with nested rows and columns with parameters v, b, r, p, q and A and abbreviated as BCBRC (v, b, r, p, q, A). He has equivalently used the condition