2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/130996This 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.Published at http://dx.doi.org/10.1214/009053605000000679 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)Statistics Theory62K15 (Primary)text