Key points are not available for this paper at this time.
Huynh Huynh, Leonard S. Feldt, Estimation of the Box Correction for Degrees of Freedom from Sample Data in Randomized Block and Split-Plot Designs, Journal of Educational Statistics, Vol. 1, No. 1 (Spring, 1976), pp. 69-82
Huynh et al. (1976) studied this question.