Fractional factorial designs of two and three levels (Q1802129)

This paper presents a survey of results on balanced fractional factorial designs (BFFD) for \(2^ m\) and \(3^ m\) series. It includes new results on search designs of \(2^ m\) type, and the survey includes the main results obtained by the reviewer, Kuwada, Shirakura, Srivastava and Yamamoto in their papers on BFFD for \(2^ m\) and \(3^ m\) series. Some open problems on the construction of fractional designs are also stated. Algebraic properties as well as the combinatorial aspects of these designs are discussed. For a given \(N\) one will come across, in general, many competing designs. In order to obtain the `best design' for \(N=N_ 0\) (`best' in some sense), optimality criteria based on the eigenvalues of the information matrices are discussed.