标题： 关于仿射全维因子设计的一些刻划 显示英文标题

标题： Some characterizations of affinely full-dimensional factorial designs

摘要： 定义了一类新的两水平非正则分数析因设计。我们称这类设计为{\it 仿射全维因子设计}，意味着该类设计中的设计点不包含在$\mathbb{F}_2$上的向量空间内的任何仿射超平面上。还阐明了此类设计的指示函数的性质。该类中的分数析因设计具有一个理想特性：主效应模型的参数可以同时可识别。我们从$D$-最优性的角度研究了该类设计的性质。特别是，对于饱和设计，在运行数量为$r \equiv 5,6,7$（模 8）的情况下，选择了$D$-最优设计。 显示英文摘要

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).