Circular designs balanced for neighbours at distances one and two
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We define three types of neighbour-balanced designs for experiments where the units are arranged in a circle or single line in space or time. The designs are balanced with respect to neighbours at distance one and at distance two. The variants come from allowing or forbidding self-neighbours, and from considering neighbours to be directed or undirected. For two of the variants, we give a method of constructing a design for all values of the number of treatments, except for some small values where it is impossible. In the third case, we give a partial solution that covers all sizes likely to be used in practice.
Aldred , R E L , Bailey , R A , Mckay , B D & Wanless , I M 2014 , ' Circular designs balanced for neighbours at distances one and two ' , Biometrika , vol. 101 , no. 4 , pp. 943-956 . https://doi.org/10.1093/biomet/asu036
Copyright 2014. Biometrika Trust. This is a pre-copyedited, author-produced PDF of an article accepted for publication in Biometrika following peer review. The version of record Circular designs balanced for neighbours at distances one and two Aldred, R. E. L., Bailey, R. A., Mckay, B. D. & Wanless, I. M. Dec 2014 In : Biometrika. 101, 4, p. 943-956 is available online at: http://biomet.oxfordjournals.org/content/101/4/943
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