Optimal main effect plans in blocks of small size

In this paper we first construct an universally optimal main effect plan (MEP) for an ssss experiment on s2(s-1)/2s2(s-1)/2 nonorthogonal blocks of size two each, s   a power of 2. Next we derive another set of sufficient conditions for an MEP on nonorthogonal blocks requiring a smaller number of blocks. These conditions are used to obtain universally optimal saturated MEPs in blocks of size 2 for (i) 4242 experiment on 6 blocks and (ii) 52×2252×22 on 10 blocks.