  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 aims at exploring the fundamental structure and
developing a theory to characterize the wordlengths and aliasing indexes for a
general $(1/4)^p$th-fraction QC design. Then the theory is applied to
(1/64)th-fraction QC designs. Examples are given, indicating that there exist
some QC designs that have better design properties, and are thus more
cost-efficient, than the regular fractional factorial designs of the same size.
In addition, a result about the periodic structure of (1/64)th-fraction QC
designs regarding resolution is stated.
