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 accompanying this paper appear online.

中文翻译：

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替代不存在的 36 种方格设计

方格设计常用于各种农作物新品种的试验。但是，对于大小为 6 的块中的 36 个品种没有用于四个或更多重复的方形点阵设计。在这里，我们使用三种不同的方法来构建最多八个重复的设计。所有的设计都表现得很好，在给出各种对比的低平均方差方面。本文随附的补充材料出现在网上。