In this paper a class of multidimensional experimental designs said to have partial factorial balance is introduced. These designs are shown to belong to the more general class of multidimensional partially balanced designs. The analysis of designs with partial factorial balance is given in detail and several series of three, four and five dimensional designs are presented.
Donald A. Anderson. "Designs with Partial Factorial Balance." Ann. Math. Statist. 43 (4) 1333 - 1341, August, 1972. https://doi.org/10.1214/aoms/1177692486