Equivalence of fractional factorial designs

Two designs for a fractional factorial experiment are equivalent if one can be obtained from the other by reordering the treatment combinations, relab eling the factors and relabeling the factor levels. Designs can be viewed a s sets of points in p-dimensional space, where p is the number of factors. It is shown that, in this setting, two designs are equivalent if the Hammin g distances between the paints are the same in all possible dimensions. An algorithm is given, based on this representation, that can detect distinct designs for 2(p) experiments without a complete search of all reorderings a nd relabelings in the fraction. In addition, if two designs are equivalent, the algorithm gives a set of permutations which map one design to the othe r.