Group testing is a method for identifying defective items from a large set by performing a relatively small number of tests on subsets of items, called pools. The collection of pools are called designs. This work explores quasi-random designs, a hybrid approach that combines the practicality of random designs with the combinatorial advantages of deterministic designs. We provide a unified theoretical explanation for various pool selection criteria involving rows and columns of design matrices in the generation of quasi-random designs with constant pool sizes. By employing linear algebraic techniques, we offer insights into the essential differences between these criteria and demonstrate their efficient implementation, addressing several computational issues encountered in previous studies. Moreover, simulations show that quasi-random designs outperform traditional random designs in noiseless group testing, even with limited pool sizes, and that the criteria proposed by Hamada and Lu (ISITA 2024) deliver the best performance in most cases, achieving higher identification accuracy and greater stability compared to the other evaluated criteria.