## The Annals of Statistics

- Ann. Statist.
- Volume 10, Number 2 (1982), 502-510.

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

#### 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.

#### Article information

**Source**

Ann. Statist., Volume 10, Number 2 (1982), 502-510.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176345791

**Digital Object Identifier**

doi:10.1214/aos/1176345791

**Mathematical Reviews number (MathSciNet)**

MR653525

**Zentralblatt MATH identifier**

0489.62068

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62K15: Factorial designs

Secondary: 05B20: Matrices (incidence, Hadamard, etc.)

**Keywords**

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

#### Citation

Galil, Z.; Kiefer, J. Construction Methods for $D$-Optimum Weighing Designs when $n \equiv 3 (\operatorname{mod} 4)$. Ann. Statist. 10 (1982), no. 2, 502--510. doi:10.1214/aos/1176345791. https://projecteuclid.org/euclid.aos/1176345791