An optimal group testing algorithm on k disjoint sets

Chang and Hwang proved that for two disjoint sets with m and n items each containing exactly one defective, thee exists a group testing algorithm to identify all defectives in ⌈log2mn⌉ tests-the information lower bound. They also showed that a similar result does not hold for k disjoint sets in general for any k≥3. In this paper the authors show that for each k there exist k disjoint sets each containing exactly one defective such that all defectives can be identified in the information lower bound number of tests.