Evaluation of Pairwise Distances Among Orthogonal Grid Points in Hypercube

摘要

This article describes an effective evaluation of pairwise distances among points that form a regular orthogonal grid inside a unit hypercube. Such an regular arrangement of points have many applications one of which is the Design of Experiments - the arrangement is known as the Full Factorial Design. The proposed process of calculation exploits the repeated point projections. Using combinatorial rules, the paper presents a closed-form exact formula that enables faster evaluation of pairwise distances and their counts compared to naive approach that enumerates the list of all possible pairs of points.