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For multifactor designs based on linear models, the information matrix generally depends on a certain set of marginal tables created from the design itself. This note considers the problems of whether a set of marginal tables is consistent, in that a design exists that can yield them, and of calculating such a design when at least one does exist. The results are obtained by direct analogy with the problem of maximum likelihood estimation in longlinear models for categorical data. [ABSTRACT FROM AUTHOR]