Bounds for threshold and majority group testing

We consider two generalizations of group testing: threshold group testing (introduced by Damaschke [8]) and majority group testing (a further generalization, including threshold group testing and a model introduced by Lebedev [15]). We show that each separating code gives a nonadaptive strategy for threshold group testing for some parameters. This is a generalization of a results on "guessing secrets", introduce. We introduce threshold codes and show that each threshold code gives a nonadaptive strategy for threshold group testing. We show that there exist threshold codes such that we can improve the lower bound for the rate of threshold group testing. We consider majority group testing if the number of defective elements is unknown (otherwise it reduces to threshold group testing). We show that cover-free codes and separating codes give strategies for majority group testing. We give a lower bound for the rate of majority group testing.