Abstract: We consider experiments run in blocks with two way heterogeneity in each block. The goal is to find ``optimal'' designs for estimating treatment effects. In this paper, a general method for constructing universally optimal nested row-column designs within the class of treatment connected designs is given. Also, a class of nested row-column designs, which has a completely symmetric information matrix but does not have maximum trace among all possible designs, is shown to have Φa-optimality for some a.
Key words and phrases: Nested row-column designs, row-column designs, universal optimality, generalized Youden designs.