Abstract: The article is devoted to the theory of the design of experiments. It introduces a formal definition of factorial models and factorial designs. On this basis, it builds the mathematical foundations of the factorial design of experiments. The presented concept supports many important aspects of experimental design including the main one: the construction of the optimal designs.
Keywords: Factorial design, factorial models, optimality of factorial designs, main effects, effects of interactions, condition of proportional frequencies, regular designs, finite euclidean space, geometric designs, definition relation, alias sets