Classification of two-level fractional fractions

The problem of finding a fraction of a two-level factorial design with specic properties is usually solved within special classes, such as regular or Plackett–Burman designs. We show that each fraction of a two-level factorial design is characterized by the ANOVA representation of its polynomial indicator function. In particular, such a representation can be used to present the problem of nding a fraction with a given orthogonality structure as the set of solutions of a system of algebraic equations. Regularity, resolution, projectivity, absence of coincidence defects can be discussed in this framework. The system of algebraic equations involved can be solved, at least in principle, using Computer Algebra softwares, such as Maple and CoCoA. As tutorial examples, all non-trivial orthogonal fractions of a 2^4 and of a 2^5 design are computed and classied.