A rectilinear equidistant set in R~d consists of points that are pairwise equidistant under the l_1-norm in R~d. Let f (d) be the maximum size of such a set. We will take tins common distance to be 2. That is,f (d) = relax{n:u_1... u _ n ∈ R ~ d ,||u_i=2 for all i It is immediate that f (d) 2d by 2d unit vectors {±e_i : 1 ≤ i ≤d} ; where {e_i : 1 ≤ i ≤ d} is the standard basis for W. In 1983, Kusner conjectured that this is the best we can do.
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机译：R〜d中的直线等距集由在R〜d中的l_1范数下成对等距的点组成。令f（d）为此类集合的最大大小。我们将锡罐的公共距离设为2。即，对于所有i，f（d）= Relax {n：u_1 ... u _ n∈R〜d，|| u_i = 2 2d x 2d单位向量{±e_i：1≤i≤d};其中{e_i：1≤i≤d}是W的标准基础。1983年，Kusner推测这是我们能做的最好的事情。
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