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The research of developing a general methodology for the construction of goodnonregular designs has been very active in the last decade. Recent research byXu and Wong [Statist. Sinica 17 (2007) 1191--1213] suggested a new class ofnonregular designs constructed from quaternary codes. This paper explores theproperties and uses of quaternary codes toward the construction ofquarter-fraction nonregular designs. Some theoretical results are obtainedregarding the aliasing structure of such designs. Optimal designs areconstructed under the maximum resolution, minimum aberration and maximumprojectivity criteria. These designs often have larger generalized resolutionand larger projectivity than regular designs of the same size. It is furthershown that some of these designs have generalized minimum aberration andmaximum projectivity among all possible designs.

Quarter-fraction factorial designs constructed via quaternary codes