## The Annals of Statistics

### Construction of optimal multi-level supersaturated designs

#### Abstract

A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and Wu [Ann. Statist. 29 (2001) 1066–1077]. A new lower bound is derived and general construction methods are proposed for multi-level supersaturated designs. Inspired by the Addelman–Kempthorne construction of orthogonal arrays, several classes of optimal multi-level supersaturated designs are given in explicit form: Columns are labeled with linear or quadratic polynomials and rows are points over a finite field. Additive characters are used to study the properties of resulting designs. Some small optimal supersaturated designs of 3, 4 and 5 levels are listed with their properties.

#### Article information

Source
Ann. Statist., Volume 33, Number 6 (2005), 2811-2836.

Dates
First available in Project Euclid: 17 February 2006

https://projecteuclid.org/euclid.aos/1140191674

Digital Object Identifier
doi:10.1214/009053605000000688

Mathematical Reviews number (MathSciNet)
MR2253103

Zentralblatt MATH identifier
1084.62070

Subjects
Primary: 62K15: Factorial designs
Secondary: 62K05: Optimal designs 05B15: Orthogonal arrays, Latin squares, Room squares

#### Citation

Xu, Hongquan; Wu, C. F. J. Construction of optimal multi-level supersaturated designs. Ann. Statist. 33 (2005), no. 6, 2811--2836. doi:10.1214/009053605000000688. https://projecteuclid.org/euclid.aos/1140191674

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