How many stratification factors are "too many" to use in a randomization plan?

The issue of stratification and its role in patient assignment has generated much discussion, mostly focused on its importance to a study [1,2] or lack thereof [3,4]. This report focuses on a much narrower problem: assuming that stratified assignment is desired, how many factors can be accommodated? This problem is investigated for two methods of balanced patient assignments; the first is based on the minimization method of Taves [5] and the second on the commonly used method of stratified assignment [6,7]. Stimulation results show that the former method can accommodate a large number of factors (10-20) without difficulty but that the latter begins to fail if the total number of distinct combination of factor levels is greater than approximately n/2. The two methods are related to a linear discriminant model, which helps to explain the results.