Asymptotics of pooling design performance

We analyse the expected performance of various group testing, or pooling, d esigns. The context is that of identifying characterized clones in a large collection of clones. Here we choose as performance criterion the expected number of unresolved 'negative' clones, and we aim to minimize this quantit y. Technically, long inclusion-exclusion summations are encountered which, aside from being computationally demanding, give little inkling of the qual itative effect of parametric control on the pooling strategy. We show that readily-interpreted re-summation can be performed, leading to asymptotic fo rms and systematic corrections. We apply our results to randomized designs, illustrating how they might be implemented for approximating combinatorial formulae.