A note on the optimality of 2-level main effects plans in blocks of odd size

In this paper we consider experimental situations where a 2-level main effects plan is to be used to study m-factors using n runs which are partitioned into b blocks of size k=n/b and where k is an odd integer. For odd k≥3 and certain cases where b is a multiple of k, we show how to construct blocked main effects plans that are optimal under most widely used optimality criteria.