The use of cyclic incomplete block designs for factorial experiments is considered. Necessary and sufficient conditions are established under which a cyclic design for an $m \times n$ factorial experiment will give an orthogonal analysis of the main effects and interaction. Various properties, the construction and analysis of such designs are then considered.
"Factorial Experiments in Cyclic Designs." Ann. Statist. 1 (1) 188 - 194, January, 1973. https://doi.org/10.1214/aos/1193342399