Optimal design with many blocking factors

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