Circular designs balanced for neighbours at distances one and two

R. E. L. Aldred*, R. A. Bailey, Brendan D. Mckay, Ian M. Wanless

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)943-956
Number of pages14
Issue number4
Early online date12 Sept 2014
Publication statusPublished - Dec 2014


  • Border plot
  • Circular design
  • Eulerian trail
  • Latin square
  • Neighbour design
  • Perfect cycle system
  • Quasigroup
  • Universal sequence


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