A problem of Kusner on equilateral sets (Q706361)

R. B. Kusner asked whether the maximum number of vectors in the \(d\)-dimensional space, with unit pairwise distance defined through the norm \(\| .\| _p\), is \(d+1\). The paper gives affirmative answer for \(p=4\), and a negative answer for \(1<p<2\), if \(d\) is sufficiently large in terms of \(p\).