Some Recent Advances on Quaternary-Code Designs

Abstract

In the recent past, there was a realization that nonregular designs could be utilized in conducting effcient experiments with exibility, run size economy, and ability to exploit interactions. This led to a growing research on developing a general construction methodology of nonregular designs with good properties. Recent work by Xu and Wong (2007) suggested a new class of nonregular designs constructed via quaternary codes. The construction methodology are parallel to regular designs, but the properties of these quaternary-code designs are at least equivalent to, or otherwise better than, regular designs of the same size in terms of resolution, aberration and projectivity. Phoa and Xu (2009) derived some important theorems about the properties of quarter-fraction quaternary-code designs. It also provided guidelines to construct optimal designs under several commonly used design criteria. This talk presents the recent developments of this new class of nonregular designs, extending the results from quarter-fraction designs to (1/8)th- and (1/16) th-fraction designs.