A new construction of 3̄-separable matrices via an improved decoding of Macula’s construction

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=3d=3 an exact probability analysis is possible. Further, we derive necessary and sufficient conditions for a positive clone to be unresolved and gave a modified construction which avoids this necessary condition, thus resulting in a 3̄-separable matrix.