Usually, in a factorial experiment, the block size of the experiments is not large enough to permit all possible treatment combinations to be included in a block. Hence we resort to the theory of confounding. With respect to symmetric factorial designs, the theory of confounding has been highly developed by Bose , Bose and Kishen  and Fisher , . An excellent summary of the results of this research appears in Kempthorne . Some examples of asymmetric factorial designs can be found in Yates , Cochran and Cox , Li , Kempthorne  and Nair and Rao , . Nair and Rao  have given the statistical analysis of a class of asymmetrical two-factor designs in considerable detail. The author  has considered the problem of achieving "complete balance" over various interactions in factorial experiments. In the present paper a class of factorial experiments, balanced factorial experiments (BFE) (Definition 4.2) is considered. The theorems proved in Section 4 outline a detailed analysis of BFE's, including estimates of various interactions at different levels. Finally, a method of constructing BFE's is given in Section 6. It should be noted that Theorems 5.2 to 5.5 are generalisations of the corresponding theorems by Zelen , and the method of construction in Section 6 is a general form of the one indicated by Yates , Nair and Rao ,  and Kempthorne  (Section 18.7).
"Balanced Factorial Experiments." Ann. Math. Statist. 31 (2) 502 - 514, June, 1960. https://doi.org/10.1214/aoms/1177705917