Symmetric and resolvable \(\lambda \)-configurations constructed from block designs (Q942118)

A \(\lambda\)-configuration \((v_r,b_k)_\lambda\) is a set \(V\) of \(v\) points and a collection \(\mathcal B\) of \(b\) \(k\)-subsets of \(V\) (\textit{blocks}) so that every point appears in precisely \(r\) blocks, and every pair of points appear together in at most \(\lambda\) blocks. When \(v=b\) (and hence \(r=k\)), the configuration is \textit{symmetric}. Different \(\lambda\)-configurations are constructed from balanced incomplete block designs; some of the resulting configurations are symmetric, while some are resolvable.