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September, 1973 Balanced Optimal Saturated Main Effect Plans of the $2^n$ Factorial and Their Relation to $(v, k, \lambda)$ Configurations
B. L. Raktoe, W. T. Federer
Ann. Statist. 1(5): 924-932 (September, 1973). DOI: 10.1214/aos/1176342512

Abstract

This paper characterizes balanced saturated main effect plans of the $2^n$ factorial in terms of $D'D$ rather than $X'X$, where $D$ is the $(n + 1) \times n$ treatment combination matrix and $X$ is the $(n + 1) \times (n + 1)$ design matrix. Besides this result, balanced optimal (in the sense of maximum determinant of $X'X$) saturated main effect plans of the $2^{4m-1}$ factorial are discussed for various classes of designs, each class consisting of designs having (0,0,$\cdots$ 0) and $n$ treatment combinations with exactly $t$ 1's among them. The optimality results are achieved by applying theorems associated with incidence matrices of $(\nu, k, \lambda)$ configurations. In addition results are given for designs associated with the permuted $(\nu, k, \lambda)$ configurations. Finally, the approach taken in the paper can be applied to $2^n$ factorials with $n \neq 4m - 1$.

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B. L. Raktoe. W. T. Federer. "Balanced Optimal Saturated Main Effect Plans of the $2^n$ Factorial and Their Relation to $(v, k, \lambda)$ Configurations." Ann. Statist. 1 (5) 924 - 932, September, 1973. https://doi.org/10.1214/aos/1176342512

Information

Published: September, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0282.05020
MathSciNet: MR339415
Digital Object Identifier: 10.1214/aos/1176342512

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 5 • September, 1973
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