Equilateral Dimension of the Rectilinear Space.

Designs Codes and Cryptography (Impact Factor: 0.73). 01/2000; 21:149-164. DOI: 10.1023/A:1008391712305
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ABSTRACT It is conjectured that there exist at most 2k equidistant points in the k- dimensional rectilinear space. This conjecture has been verified for k 3; we show here its validity in dimension k = 4. We also discuss a number of related questions. For instance, what is the maximum number of equidistant points lying in the hyperplane: P k i=1 x i = 0 ? If this number would be equal to k, then the above conjecture would follow. We show, however, that this number is k + 1 for k 4. 1

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