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A substitute for square lattice designs for 36 treatments. Bailey, Rosemary


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.

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