We consider threshold group testing – a generalization of a well known and thoroughly examined problem of combinatorial group testing. In the classical setting, the goal is to identify a set of positive individuals in a population, by performing tests on pools of elements. The output of each test is an answer to the question: is there at least one positive element inside a query set Q ? The threshold group testing is a natural generalization of this classical setting which arises when the answer to a test is positive if at least \(t>0\) elements under test are positive.