On the D-optimality of nonorthogonal blocked main effects plans

In this paper, we consider experimental situations where a main effects plan is to be used to study m two-level factors using n runs which are partitioned into b blocks of equal size k = n/b. It is shown that when $n \equiv 2 \pmod{8}$ and k > 2, the best possible design under the D-optimality criterion does not necessarily have all factors orthogonal to blocks. In such situations, an alternative class of designs is suggested for usage which are better under the D-optimality criterion than the best available design having all main effects orthogonal to blocks.