  In this paper we study optimality aspects of a certain type of designs in a
multi-way heterogeneity setting. These are ``duals" of plans orthogonal through
the block factor (POTB). Here by the dual of a main effect plan (say $\rho$) we
mean a design in a multi-way heterogeneity setting obtained from $\rho$ by
interchanging the roles of the block factors and the treatment factors.
Specifically, we take up two series of universally optimal POTBs for
symmetrical experiments constructed in Morgan and Uddin (1996). We show that
the duals of these plans, as multi-way designs, satisfy M-optimality.
  Next, we construct another series of multiway designs and proved their
M-optimality, thereby generalising the result of Bagchi and Shah (1989). It may
be noted that M-optimality includes all commonly used optimality criteria like
A-, D- and E-optimality.
