We show that for every odd integer p>_ 1 there is an absolute positive constant c.sub.p so that the maximum cardinality of a set of vectors in R.sup.n such that the l.sub.p distance between any pair is precisely 1, is at most c.sub.p n log n. We prove some upper bounds for other l.sub.p norms as well.
We show that for every odd integer p>_ 1 there is an absolute positive constant c.sub.p so that the maximum cardinality of a set of vectors in R.sup.n such that the l.sub.p distance between any pair is precisely 1, is at most c.sub.p n log n. We prove some upper bounds for other l.sub.p norms as well. (en)