Abstract
In this paper, we study some packings in a cube, namely, how to pack n points in a cube so as to maximize the minimal distance. The distance is induced by the L1-norm which is analogous to the Hamming distance in coding theory. Two constructions with reasonable parameters are obtained, by using some results from a function field including divisor class group, narrow ray class group, and so on. We also present some asymptotic results of the two packings.
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Li, H. L 1-norm packings from function fields. Sci. China Ser. A-Math. 48, 1274–1283 (2005). https://doi.org/10.1360/04ys0101
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DOI: https://doi.org/10.1360/04ys0101