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A substitute for square lattice designs for 36 treatments.

Banff International Research Station for Mathematical Innovation and Discovery

If there are $r+2$ mutually orthogonal Latin squares of order $n$ then there is a square lattice design for $n^2$ treatments in $r$ replicates of blocks of size $n$. This is optimal, and has all concurrences equal to $0$ or $1$. When $n=6$ there are no Graeco-Latin squares, and so there are no square lattice designs with replication bigger than three. As an accidental byproduct of another piece of work, Peter Cameron and I discovered a resolvable design for $36$ treatments in blocks of size six in up to eight replicates. No concurrence is greater than $2$, the design is partially balanced for an interesting association scheme with four associate classes, and it does well on the A-criterion. I will describe the design, and say something about its properties.

Mathematics; Statistics

video/mp4

Author affiliation: University of St Andrews

2018-02-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64548

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/