Miscellanea. A connection between uniformity and aberration in regular fractions of two-level factorials

Abstract

We show a link between the two apparently unrelated areas of uniformity and minimum aberration. With reference to regular fractions of two-level factorials, we derive an expression for the centred L 2 -discrepancy measure for uniformity in terms of the word-length pattern. This result indicates, in particular, excellent behaviour of minimum aberration designs with regard to uniformity and provides further justification for the popular criterion of minimum aberration.