This work shows several direct and recursive constructions of ordered covering arrays (OCAs) using projection, fusion, column augmentation, derivation, concatenation, and Cartesian product. Upper bounds on covering codes in Niederreiter–Rosenbloom–Tsfasman (shorten by NRT) spaces are also obtained by improving a general upper bound. We explore the connection between ordered covering arrays and covering codes in NRT spaces, which generalize similar results for the Hamming metric. Combining the new upper bounds for covering codes in NRT spaces and ordered covering arrays, we improve upper bounds on covering codes in NRT spaces for larger alphabets. We give tables comparing the new upper bounds for covering codes to existing ones.

中文翻译：

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有序覆盖数组和覆盖代码的上界

这项工作展示了使用投影、融合、列增强、推导、串联和笛卡尔积的有序覆盖数组 (OCA) 的几种直接和递归构造。Niederreiter–Rosenbloom–Tsfasman（用 NRT 缩短）空间中覆盖代码的上限也可以通过改进一般上限获得。我们探索了 NRT 空间中有序覆盖数组和覆盖代码之间的联系，这概括了汉明度量的类似结果。结合 NRT 空间中覆盖代码的新上限和有序覆盖数组，我们改进了 NRT 空间中更大字母表覆盖代码的上限。我们给出了表格，将覆盖代码的新上限与现有代码进行比较。