For q-ary Hamming spaces we address the problem of the minimum number of points such that any point of the space is uniquely determined by its (Hamming) distances to them. It is conjectured that for a fixed q and growing dimension n of the Hamming space this number asymptotically behaves as 2n/ log _q n. We prove this conjecture for q = 3 and q = 4; for q = 2 its validity has been known for half a century.

中文翻译：

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非二进制汉明空间的度量维

对于q元汉明空间，我们解决了最小点数的问题，使得空间中的任何点都由其到它们的（汉明）距离唯一地确定。据推测，对于固定的q和汉明空间的增长维n，该数字渐近地表现为2 n / log _q n。我们证明对于q = 3和q = 4的这种猜想；对于q = 2，其有效性已有半个世纪了。