Testing has been a major factor that limits our response to the COVID-19 pandemic. The method of sample pooling and group test has recently been introduced. However, it is still not clearly known how to determine the appropriate group size. In this paper, we develop an analytical method and a numerical algorithm to determine the optimal group size, which minimizes the total number of tests, maximizes the speedup of the pooling strategy, and minimizes both time and cost of testing. The optimal group size is determined by the fraction of infected people and independent of the size of the population. Furthermore, both the optimal pooling size and the achieved speedup grow exponentially with the reciprocal of the fraction of infected people, a quite impressive and nontrivial result. Our method is effective in supporting faster and cheaper asymptomatic COVID-19 screening. Our research has important social implications and financial impacts. For example, if the percentage of infected people is 0.001, we can achieve speedup of almost 16, which means that months of testing time can be reduced to days, and over 93% of the testing cost can be saved. Such a result has not been available in the known literature, and is a significant progress and great advance in pooling strategy optimization for accelerating asymptomatic COVID-19 screening.