正交表的线性研究

Research on the linearity of orthogonal arrays

研究了正交表的线性,讨论了线性正交表与标准正交表的关系,以及线性正交表与仿射设计之间的关系.得出如下结论:线性正交表一定是标准正交表,2水平的标准正交表是线性正交表.此外,还证明了产生1个线性正交表的1个仿射1-设计的区组的集族是1个有限仿射空间里超平面的平行组的并集.

The study on the properties of orthogonal arrays has positive function to experimentaldesign,construction and application of orthogonal arrays.Through studying the linearity of orthogonal arrays,the relationship between the linear orthogonal arrays and standard orthogonal arrays,and the relationship between the linear orthogonal arrays and the affine designs are discussed.The conclusion can be obtained which the linear orthogonal arrays must be standard,and two-level standard orthogonal arrays must be linear.It is proved that the collection of blochks of an affine 1-design that yedlds a linear orthogonal array is an union of parallel classes of hyperplanes in a finite affine space.