  This paper aims to generalize and unify classical criteria for comparisons of
balanced lattice designs, including fractional factorial designs,
supersaturated designs and uniform designs. We present a general majorization
framework for assessing designs, which includes a stringent criterion of
majorization via pairwise coincidences and flexible surrogates via convex
functions. Classical orthogonality, aberration and uniformity criteria are
unified by choosing combinatorial and exponential kernels. A construction
method is also sketched out.
