Designs for sets of experimental units with many blocking factors are studied. It is shown that if the set of blocking factors satisfies a certain simple condition then the information matrix for the design has a simple form. In consequence, a design is optimal if it is optimal with respect to one particular blocking factor and regular with respect to all the rest, in a sense which is made precise in the paper. This encompasses several previous results for optimal designs with more than one blocking factor, and applications to many other situations are given.
"Optimal design with many blocking factors." Ann. Statist. 28 (2) 553 - 577, April 2000. https://doi.org/10.1214/aos/1016218230