Work on obtaining optimal main effect plans in non-orthogonal blocks
was initiated recently by Mukerjee, Dey \& Chatterjee (2002), who gave
a set of sufficient conditions for a main effect plan to be
universally optimal under possibly non-orthogonal blocking and also
suggested a construction procedure for obtaining such block designs.
Their method is however, not applicable for all factorials. In this
paper, a new construction procedure is given for situations where the
procedure of Mukerjee et al. (2002) is inapplicable.