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 $X(n \times k)$ 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.
Citation
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. https://doi.org/10.1214/aos/1176345791
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