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June, 1982 Construction Methods for $D$-Optimum Weighing Designs when $n \equiv 3 (\operatorname{mod} 4)$
Z. Galil, J. Kiefer
Ann. Statist. 10(2): 502-510 (June, 1982). DOI: 10.1214/aos/1176345791


In the setting where the weights of $k$ objects are to be determined in $n$ weighings on a chemical balance (or equivalent problems), for $n \equiv 3 (\operatorname{mod} 4)$, Ehlich and others have characterized certain "block matrices" $C$ such that, if $X'X = C$ where $X(n \times k)$ has entries $\pm1$, then $X$ is an optimum design for the weighing problem. We give methods here for constructing $X$'s for which $X'X$ is a block matrix, and show that it is the optimum $C$ for infinitely many $(n, k)$. A table of known constructibility results for $n < 100$ is given.


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Z. Galil. J. Kiefer. "Construction Methods for $D$-Optimum Weighing Designs when $n \equiv 3 (\operatorname{mod} 4)$." Ann. Statist. 10 (2) 502 - 510, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0489.62068
MathSciNet: MR653525
Digital Object Identifier: 10.1214/aos/1176345791

Primary: 62K15
Secondary: 05B20

Keywords: $D$-optimality , 62K5 , construction methods , first order designs , fractional factorials , Optimum designs , weighing designs

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
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