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Macula proposed a novel construction of pooling designs which can effectively identify positive clones and also proposed a decoding method. However, the probability of an unresolved positive clone is hard to analyze. In this paper we propose an improved decoding method and show that for d=3 an exact probability analysis is possible. Further, we derive necessary and sufficient conditions for a positive...
Let [n] denote {1,2 n}. A set system σ on [n] is called a separating system on [n] if for each pair of distinct elements in [n], there is an M σ that contains exactly one member of that pair. A separating system τ on [n] is called totally separating if for each pair of distinct elementsj , j in [n], there are disjoint M,M τ with j M and j M . In this paper, we discuss two applications...
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