On a problem of design for screening experiments

Let a system consists of $N\gg1$ elements and $s\ll N$ of them be defective. As a result of an experiment, we can find out, if there is at least one defective element in a given set. We obtain an answer to this question, generally speaking, with an error. We must detect all defective elements with given confidence level by using the fewest number of experiments possible. In the paper, an asymptotically ($N$ being large) optimal method of design and analysis of experiments is described. A simplier method is proposed requiring insignificantly more experiments.