A colouring of a strongly regular graph is an allocation of colours (or treatments) to the vertices of the graph. Such a colouring is balanced if every pair of distinct colours occurs equally often on the ends of an edge. When the graph is the complete regular multipartite graph a balanced colouring is just a balanced incomplete-block design, or 2-design. Some constructions are given. For examp...

(v,5, 1) RBI BDs were known to exist for all but 109 values of v == 5 mod 20. Solutions are given for all but 6 of these. Also given is a new (45,5,3) RBIBD plus some new incomplete TDs, 14 new (v,6,1) BIBDs and some new PBDs with K = {6} u {Prime powers == 1 mod 5}. A design is a pair (X,5l) where X is a finite set (whose elements are called paints) and .9[ is a collection of subsets of X (cal...