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.
Publié le : 1982-06-14
Classification:
62K5,
Optimum designs,
weighing designs,
construction methods,
$D$-optimality,
first order designs,
fractional factorials,
62K15,
05B20
@article{1176345791,
author = {Galil, Z. and Kiefer, J.},
title = {Construction Methods for $D$-Optimum Weighing Designs when $n \equiv 3 (\operatorname{mod} 4)$},
journal = {Ann. Statist.},
volume = {10},
number = {1},
year = {1982},
pages = { 502-510},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345791}
}
Galil, Z.; Kiefer, J. Construction Methods for $D$-Optimum Weighing Designs when $n \equiv 3 (\operatorname{mod} 4)$. Ann. Statist., Tome 10 (1982) no. 1, pp. 502-510. http://gdmltest.u-ga.fr/item/1176345791/