  For large classes of group testing problems, we derive lower bounds for the
probability that all significant factors are uniquely identified using
specially constructed random designs. These bounds allow us to optimize
parameters of the randomization schemes. We also suggest and numerically
justify a procedure of construction of designs with better separability
properties than pure random designs. We illustrate theoretical consideration
with large simulation-based study. This study indicates, in particular, that in
the case of the common binary group testing, the suggested families of designs
have better separability than the popular designs constructed from the disjunct
matrices.
