The n X n X n Dots Problem: An Improved “Outside the Box” Upper Bound
Marco Ripà, Valerio Bencini · viXra · 2018
In this paper we describe two new patterns, in order to improve the upper bound for the Ripa’s n X n X n points problem, saving a few lines for many values of n. The new upper bound, for any n≥6, becomes h_u(n)=int((3/2*n^2)+int(n/4)-int((n-1)/4)+int((n+1)/4)-int((n+2)/4)+n-2, where int(x)≔floor(x).