Superimposed codes and combinatorial group testing

In the error detection/correction version of the problem, some group tests are permitted to report “false positives”; an a priori bound q on the number of such false positives is assumed. 56.23 Theorem [147, 764] (V, B) is a solution to the strict group testing problem with threshold p and error detection (correction) for q false positives if and only if, for every union of p or fewer blocks, every other block contains at least q + 1 (2q + 1, respectively) points not in this union. Hence, any packing (V, B) of t-sets into k-sets having k ≥ p(t − 1) + q + 1 (k ≥ p(t − 1) + 2q + 1, respectively) is a solution to the strict group testing problem with threshold p and error detection (correction, respectively) for q false positives.