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Some characterizations of affinely full-dimensional factorial designs

Satoshi Aoki
Akimichi Takemura
Abstract

A new class of two-level non-regular fractional factorial designs is defined. We call this class an {\it affinely full-dimensional factorial design}, meaning that design points in the design of this class are not contained in any affine hyperplane in the vector space over F2\mathbb{F}_2. The property of the indicator function for this class is also clarified. A fractional factorial design in this class has a desirable property that parameters of the main effect model are simultaneously identifiable. We investigate the property of this class from the viewpoint of DD-optimality. In particular, for the saturated designs, the DD-optimal design is chosen from this class for the run sizes r5,6,7r \equiv 5,6,7 (mod 8).

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