A quaternary linear code is a linear space over the ring of integers modulo
4. Recent research in coding theory shows that many famous nonlinear codes such
as the Nordstrom and Robinson (1967) code and its generalizations can be simply
constructed from quaternary linear codes. This paper explores the use of quaternary
codes to construct two-level nonregular designs. A general construction of nonregular
designs is described and some theoretic results are obtained. Many nonregular designs
constructed by this method have better statistical properties than regular designs of the
same size in terms of resolution, aberration and pro jectivity. A systematic construction
procedure is proposed and a collection of nonregular designs with 16, 32, 64, 128 and
256 runs is presented.