Improved Quasi-Random Designs with Constant Pool Sizes for Group Testing

Group testing is a well-studied approach for identifying defective items among a large amount of items by conducting a relatively small number of tests on pools of items. In this paper, we propose a novel method for generating quasi-random designs with constant pool sizes for noiseless non-adaptive group testing. Our approach incorporates insights from combinatorial properties to optimize the distribution of Hamming distances in pooling designs. Simulations with established practical decoding algorithms show that our quasi-random designs outperform existing random and quasi-random methods in both identification accuracy and stability. These improved designs have the potential to provide significant benefits for real-world applications of group testing, such as PCR testing in large populations and network security.