AESTRACTThis paper extends metQods of constructing confounded and lattice designs for the symmetrical factorial to the asymmetrical or mixed factorial. Beside providing unifying techniques some enumeration results are also given along with a fully discussed non-trivial example. In bringing about this extension and unification the usual Galois field theory was modified to ring theory; cyclic collineations as used in £-restrictional lattice designs were adapted to the mixed factorial case.