Two-level fractional factorial designs are a popular tool to explore the effects of many factors in a small number of experimental runs. The most common guide to choosing a fractional design is its resolution, which describes the extent to which effects of different order are aliased with one another. To choose among designs with the same resolution, Fries and Hunter proposed the criterion of minimum aberration. This criterion, like resolution, can be defined by a combinatorial property of the defining relation of a two-level fractional factorial design. Does this combinatorial property actually lead to a statistically efficient design? In this talk I will discuss two efficiency criteria and will show that minimum aberration designs are optimal, or nearly optimal, with respect to both.

This is joint work with Ching-Shui Cheng and Don Sun.