Random and quasi-random designs in group testing

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