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# Construction Methods for D-Optimum Weighing Designs when $n \equiv 3 (\operatorname{mod} 4)$

Z. Galil and J. Kiefer
The Annals of Statistics
Vol. 10, No. 2 (Jun., 1982), pp. 502-510
Stable URL: http://www.jstor.org/stable/2240684
Page Count: 9
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## Abstract

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 × 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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