A new method of constructing Sudoku tables (STs) (Sudoku Latin squares) is introduced by making use of individual vectors of cyclotomic cosets of $Z_n$ and their Kronecker product. We show that, it is possible to construct $m$ different STs of order $m$ such that for every $0\leq u, v \leq m-1$ the $(u, v)$-entry of these $m$ STs is different. These STs could be considered as a perfect set of strongly mutually distinct (SMD) STs, which in turn are used to construct a solid Sudoku cube $(\text{SSC})$. As a result, a new version of SMD Sudoku puzzles under a new rule and condition is introduced that are interesting for Sudoku puzzles game designers.

中文翻译：

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用Cyclotomic Cosets构造强互不相同的数独表和实心数独立方体

介绍了一种构造数独表 (ST)（数独拉丁方）的新方法，该方法是利用 $Z_n$和他们的 Kronecker 产品。我们证明，可以构造百万美元 不同顺序的 ST 百万美元 这样对于每个 $0\leq u, v \leq m-1$ 这 $(u, v)$- 这些条目 百万美元ST不一样。这些 ST 可以被视为一组完美的强互不相同 (SMD) ST，而这些 ST 又可用于构建实心数独立方体$(\text{SSC})$. 因此，在新规则和条件下引入了新版本的 SMD 数独谜题，这对数独谜题游戏设计师来说很有趣。