Optimal main effect plans in nested row-column set-up of small size

In many experimental situations, there are two blocking factors nested within another blocking factor. This is termed nested row-column set-up. The available factorial designs in such a set-up are large and so may not always be practically useful. We consider factorial designs in these set-ups where the number of levels of each factor, including the blocking factor, is small and obtain main effect plans which are optimal for the estimation of all the treatment factors.