A note on uniformity and orthogonality

Fang et al. (Technometrics 42 (2000) 237) proposed a united approach for searching orthogonal fractional factorial designs. They conjecture an important "equivalence theorem" between the uniformity of experimental points over the domain and the design orthogonality. They showed numerically that uniformity of experimental points over the domain can imply design orthogonality and conjecture that every orthogonal design can be obtained by minimizing some measure of uniformity. This paper shows that their conjecture is only true in some special cases.