In addition to the assumptions that we already talked about this design assumes:
Two or more factors, each factor having two or more levels.
All levels of each factor are investigated in combination with all levels of every other factor. If there are a (= 3) levels of factor A and b (= 3) levels of factor B then the experiment contains a x b (= 3 x 3 = 9) combinations. (the treatment levels are completely crossed).
Random assignment of experimental units to treatment combinations. Each experimental unit must be assigned to only one combination