Substitutes for the non-existent square lattice designs for 36 varieties

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

doi:10.1007/s13253-020-00388-1

Substitutes for the non-existent square lattice designs for 36 varieties

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

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Abstract

Square 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.

Original language	English
Pages (from-to)	487-499
Number of pages	13
Journal	Journal of Agricultural, Biological and Environmental Statistics
Volume	25
Issue number	4
Early online date	4 Mar 2020
DOIs	https://doi.org/10.1007/s13253-020-00388-1
Publication status	Published - Dec 2020

Keywords

A-optimality
Computer search
Resolvable block designs
Semi-Latin squares
Sylvester graph

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10.1007/s13253-020-00388-1Licence: CC BY

Bailey2020_Article_SubstitutesForTheNon-existentS
Copyright © 2020 the Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Final published version, 549 KBLicence: CC BY

Cite this

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abstract = "Square 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.",

keywords = "A-optimality, Computer search, Resolvable block designs, Semi-Latin squares, Sylvester graph",

author = "Bailey, {R. A.} and Cameron, {Peter J.} and Soicher, {L. H.} and Williams, {E. R.}",

note = "Funding: UK EPSRC grant EP/M022641/1 (CoDiMa: a Collaborative Computational Project in the area of Computational Discrete Mathematics).",

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N2 - Square 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.

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KW - Resolvable block designs

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KW - Sylvester graph

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Substitutes for the non-existent square lattice designs for 36 varieties

Abstract

Keywords

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CoDiMa: CoDiMa (CCP in the area of Computational Discrete Mathematics)

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Substitutes for the non-existent square lattice designs for 36 varieties

Abstract

Keywords

Access to Document

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Projects

CoDiMa: CoDiMa (CCP in the area of Computational Discrete Mathematics)

Cite this