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.

翻译：对于大类群体测试问题,我们从所有重要因素使用特殊随机设计被独特识别的概率中得出较低的界限,这些界限使我们能够优化随机化计划的参数;我们还提出并用数字说明建造设计过程的分离性强于纯随机设计。我们用大型模拟研究来说明理论考虑。特别是,在普通的二元组测试中,建议的设计组别比从分离矩阵中制造的流行设计更具有分离性。