New results and applications of superimposed codes (and related combinatorial structures) to the design of efficient group testing procedures

Let s be the number of unknown positive elements in a population of n members, 2/spl les/s<n. We aim at finding all the s positive elements by testing group of members of the population, under the constraint that a group tests positive if and only if it contains exactly one positive element. This model was considered in [T. Berger et al., 1984, P. Damaschke, 1998]. We provide tight upper and lower bounds on the optimal number of tests needed to solve above group testing problem, improving on [A.G. Dyachkov, 2003]. Instrumental to our results are new and improved bounds for generalized superimposed codes in the sense of [A. De Bonis et al., 2003, A.G. Dyachkov et al., 1984].