  Factorial designs have broad applications in agricultural, engineering and
scientific studies. In constructing and studying properties of factorial
designs, traditional design theory treats all factors as nominal. However, this
is not appropriate for experiments that involve quantitative factors. For
designs with quantitative factors, level permutation of one or more factors in
a design matrix could result in different geometric structures, and, thus,
different design properties. In this paper indicator functions are introduced
to represent factorial designs. A polynomial form of indicator functions is
used to characterize the geometric structure of those designs. Geometric
isomorphism is defined for classifying designs with quantitative factors. Based
on indicator functions, a new aberration criteria is proposed and some minimum
aberration designs are presented.
