This chapter provides the mathematical and statistical background for designs that are constructed by the FACTEX procedure; it also outlines the search algorithm that is used to find suitable construction rules. The material in this chapter is general and theoretical; you do not need to read this chapter to use the procedure for constructing most common experimental designs. On the other hand, you might want to read this chapter for the following reasons:

• to understand the general structure of designs that can be constructed with the FACTEX procedure

• to construct designs for factors with more than two levels, especially if interactions are involved

• to improve the search used by the procedure when constructing complicated designs involving many factors