仿射全维析因设计的一些特征
Some characterizations of affinely full-dimensional factorial designs
摘要：
定义了一类新的两水平非正则部分析因设计。我们称这个类为{ \it仿射全维析因设计}，这意味着这个类的设计中的设计点不包含在$\mathbb{F}_2$上的向量空间中的任何仿射超平面中。还阐明了该类的指示器函数的属性。这类部分因子设计具有理想的属性，即主效应模型的参数同时可识别。我们从$D$ -最优性的角度研究了这类问题的性质。特别是，对于饱和设计，$D$ -最优设计是针对试验规模$r \equiv 5,6,7$（mod 8）从此类中选择的。
英文摘要：
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 $\mathbb{F}_2$. 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 $D$-optimality. In particular, for the saturated designs, the $D$-optimal design is chosen from this class for the run sizes $r \equiv 5,6,7$ (mod 8).
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