| Shah and Sinha (1993) found a set of sufficient conditions for universally optimal designs (for comparing treatment effects) to exist in the usual fixed effects 3-factor additive model. But, their proof of the existence of such optimal designs is complicated and last four pages long. In this paper, we explore the theory of system of distinct representatives (SDRs) to derive the proof. Under some restrictions of row-column patterns, a systematic universally optimal row-column designs construction method is also obtained. |