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

TL;DR

This paper develops alternative experimental designs for 36 crop varieties in agricultural trials, addressing the lack of existing square lattice designs for certain block and replicate configurations.

Contribution

It introduces three novel approaches to construct efficient designs for 36 varieties with up to eight replicates, filling a gap in experimental design options.

Findings

All proposed designs achieve low average variance of variety contrasts.

Designs are effective for trials with up to eight replicates.

The methods expand options for agricultural experiment planning.

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. Supplementary materials are available online.