E ach treatment only occurs one time in one sequence, in one period. In Williams design with an even number of n treatment groups, there will be n number of sequences or an "n by n" square. With the limited sample size, the Williams design is the most efficient design and minimizes the potential impact of the carryover effect.
In a SAS SUGI paper " Generating Randomization Schedules Using SAS Programming", I described how to use SAS program to construct the randomization schedule for a study with Williams design. In one of my previous posts, I described the Williams design and its usefulness in phase I or clinical pharmacology studies. The most number of treatment groups I see is a study with 6 treatment groups. It is unlikely to have a clinical trial with 26 treatment groups. Courtesy from the website, the list below contains the Williams design with 2 to 26 treatment groups.
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