Isomorphism Check for $2^n$ Factorial Designs with Randomization Restrictions.

Factorial designs with randomization restrictions are often used in industrial experiments when complete randomization of trials is impractical. In the statistics literature, the analysis, construction and isomorphism of factorial designs have been extensively investigated. Much of the work has been on a case-by-case basis -- addressing completely randomized designs, randomized block designs, split-plot designs, etc. separately. In this paper we take a more unified approach, developing theoretical results and an efficient relabeling strategy to both construct, and check the isomorphism of, multi-stage factorial designs within a unified framework. The examples presented in this paper particularly focus on split-lot designs.