Ehrenfeld and Zacks  presented randomized procedures for regular fractions and Zacks ,  showed that an unbiased estimator of a given parameter vector in the saturated fractional replicate case exists only if one randomizes over all possible designs of a certain structure. In this paper, a similar method to the Randomized Procedure I in their paper is given for the saturated irregular main effect fractional replicates and an unbiased estimator of the main effect parameter vector is presented. Prior to this presentation, an invariant property of the information matrix is investigated. The explicit expression of the variance of the estimator is a remaining problem.
U. B. Paik. W. T. Federer. "A Randomized Procedure of Saturated Main Effect Fractional Replicates." Ann. Math. Statist. 41 (2) 369 - 375, April, 1970. https://doi.org/10.1214/aoms/1177697077