期刊
ANNALS OF STATISTICS
卷 33, 期 6, 页码 2811-2836出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/009053605000000688
关键词
Addelman-Kempthorne construction; additive character; Galois field; generalized minimum aberration; orthogonal array; supersaturated design
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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