Universally optimal structurally balanced row-column designs with some empty nodes

In this paper, we present two methods of construction of a class of universally optimal b1×b2 row-column designs with b2-k1>0 empty nodes in each row and b1-k2>0 empty nodes in each column. The number of treatments under consideration is of the form s+1 where s is an odd prime power number. The designs constructed here are structurally balanced in the sense that every pair of columns is used in an equal number of rows. The proposed designs can also be used as universally optimal two-factor orthogonal main-effect plans arranged in incomplete blocks which are also equivalent to orthogonal pairs of balanced incomplete block designs, balanced incomplete block designs for two sets of treatments, and two stage experiments in incomplete blocks with different numbers of treatments for the two stages.