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December 2005 Construction of optimal multi-level supersaturated designs
Hongquan Xu, C. F. J. Wu
Ann. Statist. 33(6): 2811-2836 (December 2005). DOI: 10.1214/009053605000000688


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.


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Hongquan Xu. C. F. J. Wu. "Construction of optimal multi-level supersaturated designs." Ann. Statist. 33 (6) 2811 - 2836, December 2005.


Published: December 2005
First available in Project Euclid: 17 February 2006

zbMATH: 1084.62070
MathSciNet: MR2253103
Digital Object Identifier: 10.1214/009053605000000688

Primary: 62K15
Secondary: 05B15 , 62K05

Keywords: Addelman–Kempthorne construction , additive character , Galois field , generalized minimum aberration , orthogonal array , supersaturated design

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.33 • No. 6 • December 2005
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