具有（弱）最小象差的分辨IV的$2^{n-m}$设计的一些结果
Some results on $2^{n-m}$ designs of resolution IV with (weak) minimum aberration
摘要：
众所周知，试验规模为$N=2^{n-m}$的所有分辨率IV正则$2^{n-m}$设计，其中$5N/16<n<N/2$必须是具有$N/2$因子的最大偶数设计的投影，因此是偶数设计。本文导出了任意偶数$2^{n-m}$设计的字长模式与其极大偶数设计的补设计的字长模式之间的一个一般而明确的关系。利用这些恒等式，我们确定了一些（弱）最小像差$2^{n-m}$设计的分辨率IV和它们的互补设计的结构。在此基础上，构造了几类分辨率为IV的最小像差$2^{n-m}$设计。
英文摘要：
It is known that all resolution IV regular $2^{n-m}$ designs of run size $N=2^{n-m}$ where $5N/16<n<N/2$ must be projections of the maximal even design with $N/2$ factors and, therefore, are even designs. This paper derives a general and explicit relationship between the wordlength pattern of any even $2^{n-m}$ design and that of its complement in the maximal even design. Using these identities, we identify some (weak) minimum aberration $2^{n-m}$ designs of resolution IV and the structures of their complementary designs. Based on these results, several families of minimum aberration $2^{n-m}$ designs of resolution IV are constructed.
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