Circular designs balanced for neighbours at distances one and two

Rosemary Bailey, University of St Andrews

Richard Cormack posed me the following problem in 1993. A marine biologist wants to suspend 5 replicates of 5 types of bryozoan around the circumference of a cylindrical tank in such a way that all ordered pairs occur once at distance one and once at distance two. I shall begin with some general issues in the design and analysis of experiments where neighbour effects are expected, and then discuss the general solution to the original problem with 5 replaced by $n$.