Minimal pairwise balanced designs (Q908918)

Consider a pairwise balanced design on v elements with \(\lambda =1\) in which k denotes the size of the longest block(s). The minimum number of blocks in such a design is denoted by \(g^{(k)}(1,2;v)\). By some counting arguments and algebraic manipulations the author obtains an expression for \(g^{(k)}(1,2;v)\) involving a certain remainder term. From this expression he derives earlier bounds and other results in a rather unified way.