Construction of some [formula omitted]-level regular designs with general minimum lower-order confounding

Abstract

Based on an aliased component-number pattern (ACNP), a general minimum lower-order confounding (GMC) criterion has been proposed to choose the optimal regular designs, which minimize the confounding among lower-order effects. This paper is ready to study the properties of GMC s-level designs in terms of complementary sets. It is proved that an sn−m design has GMC only if its complementary set is contained in a flat. Then some GMC sn−m designs are constructed when n=(N−sr)∕(s−1)+t and 0≤t≤(sr−sr−1)∕(s−1), where N=sn−m and r<n−m. These results are further illustrated with some examples.