Substitutes for the Non-existent Square Lattice Designs for 36 Varieties

Author:

Bailey R. A.ORCID,Cameron Peter J.ORCID,Soicher L. H.,Williams E. R.

Abstract

AbstractSquare lattice designs are often used in trials of new varieties of various agricultural crops. However, there are no square lattice designs for 36 varieties in blocks of size six for four or more replicates. Here, we use three different approaches to construct designs for up to eight replicates. All the designs perform well in terms of giving a low average variance of variety contrasts.Supplementary materials accompanying this paper appear online.

Funder

Engineering and Physical Sciences Research Council

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Statistics, Probability and Uncertainty,General Agricultural and Biological Sciences,Agricultural and Biological Sciences (miscellaneous),General Environmental Science,Statistics and Probability

Reference35 articles.

1. Bailey, R. A. (1990) An efficient semi-Latin square for twelve treatments in blocks of size two. Journal of Statistical Planning and Inference26, 263–266.

2. Bailey, R. A. (1997) A Howell design admitting $$A_5$$. Discrete Mathematics167/168, 65–71.

3. Bailey, R. A. (2004) Association Schemes: Designed Experiments, Algebra and Combinatorics. Cambridge: Cambridge University Press.

4. Bailey, R. A. and Cameron, P. J. (2018) Substitutes for the non-existent square lattice designs for $$36$$ varieties. Biuletyn Oceny Odmian35, 11–13.

5. Bailey, R. A., Cameron, P. J. and Nilson, T. (2018) Sesqui-arrays, a generalisation of triple arrays. Australasian Journal of Combinatorics71, 427–451.

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