  The joint use of counting functions, Hilbert basis and Markov basis allows to
define a procedure to generate all the fractions that satisfy a given set of
constraints in terms of orthogonality. The general case of mixed level designs,
without restrictions on the number of levels of each factor (like primes or
power of primes) is studied. This new methodology has been experimented on some
significant classes of fractional factorial designs, including mixed level
orthogonal arrays.
