四进制码设计的三角法及其对八分之一和十六分之一分数的应用
A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions
摘要：
在过去的二十年里，对良好的非正则部分析因设计的研究受到了极大的关注。最近的研究表明，从四元码（QC）构造的设计在这方面是非常有前途的。本文展示了如何三角的方法，可以促进系统的理解，这样的QC设计，并导致新的理论成果，涵盖迄今未探索的情况。我们把注意力集中在八分之一和十六分之一的两级因子，并表明，最佳的QC设计往往有更大的广义分辨率和投影比可比的常规设计。此外，这些设计中的一些被发现有最大的投影在所有的设计。
英文摘要：
The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The present paper shows how a trigonometric approach can facilitate a systematic understanding of such QC designs and lead to new theoretical results covering hitherto unexplored situations. We focus attention on one-eighth and one-sixteenth fractions of two-level factorials and show that optimal QC designs often have larger generalized resolution and projectivity than comparable regular designs. Moreover, some of these designs are found to have maximum projectivity among all designs.
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