Abstract Augmented designs play an important role in early-generation plant breeding when many varieties are tested and sufficient seeds are unavailable to permit each variety to be replicated more than once. The key idea is to include some replicated varieties to adjust for environmental heterogeneity and provide a good estimate of error. The simplest form of augmented design is constructed using randomized complete blocks for a few replicated varieties and augmenting each block with unreplicated varieties. This idea is readily extended to incomplete-block designs and row-column designs. A challenge is to ensure good coverage of the experimental field with replicated varieties. A problem with augmented row-column designs is that replicated variety plots may be clustered in parts of the field. One way to improve the evenness of replicated variety plot distribution is to use regions as a third blocking factor, formed by intersection of row groups (i.e. groups of adjacent rows) and column groups (i.e. groups of adjacent columns). First, a strategy to identify the numbers of regions, row groups, and column groups is proposed. Second, a general approach to search for augmented designs with three blocking factors for any numbers of unreplicated varieties and replicated varieties is presented. Finally, the algorithm is illustrated for common scenarios in plant breeding.

中文翻译：

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现场试验中的增强准数独设计

摘要 增强设计在早期植物育种中发挥着重要作用，当许多品种被测试并且没有足够的种子来允许每个品种被复制不止一次时。关键思想是包括一些复制品种以调整环境异质性并提供良好的误差估计。最简单的增强设计形式是使用随机完整块来构建一些复制品种，并用未复制的品种增加每个块。这个想法很容易扩展到不完整块设计和行列设计。一个挑战是确保复制品种对试验田的良好覆盖。增强行列设计的一个问题是重复的品种图可能聚集在部分田地中。提高复制品种地块分布均匀性的一种方法是使用区域作为第三个分块因子，由行组（即相邻行组）和列组（即相邻列组）的交集形成。首先，提出了一种识别区域、行组和列组数量的策略。其次，提出了一种针对任意数量的未复制品种和复制品种搜索具有三个分块因子的增强设计的通用方法。最后，针对植物育种中的常见场景说明了该算法。和列组被提议。其次，提出了一种针对任意数量的未复制品种和复制品种搜索具有三个分块因子的增强设计的通用方法。最后，针对植物育种中的常见场景说明了该算法。和列组被提议。其次，提出了一种针对任意数量的未复制品种和复制品种搜索具有三个分块因子的增强设计的通用方法。最后，针对植物育种中的常见场景说明了该算法。