On the D-optimality of orthogonal and 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. For the case n≡2(mod8) and k>2 where k is even, sufficient conditions are derived for certain designs having all main effects orthogonal to blocks to be D-optimal among all available designs. For n≡2(mod8) we also give conditions under which one type of design not having all main effects orthogonal to blocks is D-optimal among all available designs.