The rectangular spiral or the $n_1\times n_2\times \cdots \times n_k$ Points Problem

A generalization of Ripà’s square spiral solution for the $n\times n\times \cdots \times n$ Points Upper Bound Problem. Additionally, we provide a non-trivial lower bound for the $k$-dimensional $n_1\times n_2\times \cdots \times n_k$ Points Problem. In this way, we can build a range in which, with certainty, all the best possible solutions to the problem we are considering will fall. Finally, we give a few characteristic numerical examples in order to appreciate the fineness of the result arising from the particular approach we have chosen.