Protection against premature termination of experiments based on Williams squares with circular structure

Abstract

It is known that Williams squares with circular structure are E-optimal in certain circumstances. We introduce a particular type of Williams square with circular structure called a witch-hat square which may be preferable to other Williams squares with circular structure if it is possible that the experiment may be terminated prematurely, We show that witch-hat squares exist for all n, where n ≠ 4k, give some enumeration results for small n and report that a computer search has shown that there are no witch-hat squares of order 8 (it is known that there are no Williams squares with circular structure of order 4).