A partition testing strategy divides the program's input domain into subdomains according to a partitioning scheme, and selects test cases from each subdomain according to a test allocation scheme. Previous studies have shown that partition testing strategies can be very effective or very ineffective in detecting faults, depending on both the partitioning scheme and the test allocation scheme. Given a partitioning scheme, the maximin criterion chooses a test allocation scheme that will maximally improve the lower bound performance of the partition testing strategy. In an earlier work, we have proved that the Basic Maximin Algorithm can generate such a test allocation scheme. In this paper, we derive further properties of the Basic Maximin Algorithm and present the Complete Maximin Algorithm that generates all possible test allocation schemes that satisfy the maximin criterion.