Minimal generating set size (Dan Dima)

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Take all the points having integer coordinates (i,j,k) , 0 <= i,j,k <= N - inside a cube C of length N. (N=10 to 100) Part 1(A). Find a minimal generating set A such that: any point in C lies on some line generated by two points from A. Part 2(B). Find a minimal generating set B such that: for any points x,y from B then all the points from C also on the line xy will belong to B. Please send us a simpler description.