Construction of optimal multi-level supersaturated designs

The Annals of Statistics · 2005 · Volume 33 · Issue 6

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.

Keywords

05B15, 62K05, 62K15, Addelman–Kempthorne construction, additive character, Galois field, generalized minimum aberration, orthogonal array, supersaturated design

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