We complete the classification of tight 4-designs in Hamming association schemes H ( n , q ), i.e., that of tight orthogonal arrays of strength 4, which had been open since a result by Noda (1979). To do so, we construct an association scheme attached to a tight 4-design in H ( n , q ) and analyze its triple intersection numbers to conclude the non-existence in all open cases.

中文翻译：

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论汉明关联方案中的紧 4-设计

我们完成了汉明关联方案 H ( n , q ) 中紧 4 设计的分类，即强度为 4 的紧正交阵列的分类，自 Noda (1979) 的结果以来一直是开放的。为此，我们在 H ( n , q ) 中构建了一个与紧密 4 设计相关的关联方案，并分析其三重交叉数以得出在所有开放案例中都不存在的结论。