用四元码构造的四分之一因子设计
Quarter-fraction factorial designs constructed via quaternary codes
摘要：
在过去的十年里，发展一种构造良好的非正则设计的通用方法的研究一直非常活跃。最近的研究徐和黄[统计。Sinica 17（2007）1191- 1213]提出了一类新的由四元码构造的非正则设计.本文探讨了四元码的性质及其在构造四分之一分式非正则设计中的应用。关于这种设计的混叠结构，得到了一些理论结果。在最大分辨率、最小像差和最大投影准则下构造了最优设计。这些设计通常比相同尺寸的常规设计具有更大的广义分辨率和更大的投影率。它进一步表明，这些设计中的一些具有广义最小像差和最大的投影在所有可能的设计。
英文摘要：
The research of developing a general methodology for the construction of good nonregular designs has been very active in the last decade. Recent research by Xu and Wong [Statist. Sinica 17 (2007) 1191--1213] suggested a new class of nonregular designs constructed from quaternary codes. This paper explores the properties and uses of quaternary codes toward the construction of quarter-fraction nonregular designs. Some theoretical results are obtained regarding the aliasing structure of such designs. Optimal designs are constructed under the maximum resolution, minimum aberration and maximum projectivity criteria. These designs often have larger generalized resolution and larger projectivity than regular designs of the same size. It is further shown that some of these designs have generalized minimum aberration and maximum projectivity among all possible designs.
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