Saturated fractions of two-factor designs

In this paper we study saturated fractions of a two-factor design under the simple effect model. In particular, we define a criterion to check whether a given fraction is saturated or not, and we compute the number of saturated fractions. All proofs are constructive and can be used as actual methods to build saturated fractions. Moreover, we show how the theory of Markov bases for contingency tables can be applied to two-factor designs for moving between the designs with given margins.