Abstract: When designing an experiment, it is important to choose a design that is optimal under model uncertainty. The general minimum lower-order confounding (GMC) criterion can be used to control aliasing among lower-order factorial effects. A characterization of GMC via complementary sets was considered in Zhang and Mukerjee (2009a); however, the problem of constructing GMC designs is only partially solved. We provide a solution for two-level factorial designs withfactors and
runs subject to a restriction on
:
. The construction is quite simple: every GMC design, up to isomorphism, consists of the last
columns of the saturated
design with Yates order. In addition, we prove that GMC designs differ from minimum aberration designs when
satisfies either of the following conditions: (i)
, or (ii)
,
with
.
Key words and phrases: Aliased effect-number pattern, effect hierarchy principle, fractional factorial design, minimum aberration, resolution, wordlength pattern, Yates order.