This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in 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.

翻译：这项工作展示了利用投影、聚变、柱增殖、衍生、凝聚和笛卡尔产品对定购覆盖阵列进行的若干直接和循环构造。通过改进一般的上界,也可以获得NRT空间覆盖代码的上界。我们探索定购覆盖阵列与NRT空间覆盖代码的上界之间的联系,后者为Hamming 度量的类似结果作了概括。结合了NRT空间覆盖代码和定购覆盖阵列的新上界,我们改进了NRT空间覆盖较大字母的代码的上界。我们给出了将覆盖代码的新上限与现有代码进行比较的表格。