Abstract

It is shown that in general, with arbitrary levels of quantitative treatment factor, the constant block-sum balanced incomplete block designs do not exist. I then provide, assuming it exists, a general approach to construct a constant block-sum equireplicated block design, possibly with unequally spaced treatments, from the incidence matrix of a block design with same parameters but without constant block-sum property. I illustrate the nuances of obtaining a solution or establishing its nonexistence via several examples of partially balanced incomplete block designs.

中文翻译：

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关于等重复常数块和设计的构造

摘要

结果表明，一般而言，对于任意水平的定量处理因子，不存在恒定区组和平衡不完全区组设计。然后，假设存在，我提供了一种通用方法来构造一个可能具有不等间距处理的恒定块和等重复块设计，该方法从具有相同参数但没有恒定块和属性的块设计的关联矩阵。我通过几个部分平衡的不完全块设计示例来说明获得解决方案或确定其不存在的细微差别。