A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions
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.
UNIFORM FOUR-LEVEL DESIGNS FROM TWO-LEVEL DESIGNS : A NEW LOOK
Literature reviews reveal that the research on the issue of constructing efficient uniform designs has been very active in the last decade. In addition, coding theory is widely used in the context of constructing good optimal designs. The present paper explores the construction of highly efficient four-level uniform designs via two transformations: a modified Gray map code and a mapping between quaternary codes and the sequence of three binary codes. Efficiency is based on uniformity measured by the centered L2and wrap-around L2-discrepancies of the four-level designs’ binary images. Some results related to the lower bounds of the uniformity measures for such designs are also considered in this study.
Design Selection and Classification for Hadamard Matrices Using Generalized Minimum Aberration Criteria
Deng and Tang (1999) and Tang and Deng (1999) proposed and justified two criteria of generalized minimum aberration for general two-level fractional factorial designs. The criteria are defined using a set of values called J characteristics. In this article, we examine the practical use of the criteria in design selection. Specifically, we consider the problem of classifying and ranking designs that are based on Hadamard matrices. A theoretical result on J characteristics is developed to facilitate the computation. The issue of design selection is further studied by linking generalized aberration with the criteria of efficiency and estimation capacity. Our studies reveal that generalized aberration performs quite well under these familiar criteria.