This paper deals with combinatorial aspects of designs for two-way elimination of heterogeneity for making all possible paired comparisons of treatments belonging to two disjoint sets of treatments. Balanced bipartite row-column (BBPRC) designs have been defined which estimate all the elementary contrasts involving two treatments one from each of the two disjoint sets with the same variance. General efficiency balanced row-column designs (GEBRC) are also defined. Some general methods of construction of BBPRC designs have been given using the techniques of reinforcement, deletion (addition) of column or row structures, merging of treatments, balanced bipartite block (BBPB) designs, juxtaposition, etc. Some methods of construction give GEBRC designs also.
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