It's an interesting idea, but I think it would prove to be equivalent. As another commenter pointed out, the efficiency of this operation really only matters i

It's an interesting idea, but I think it would prove to be equivalent. As another commenter pointed out, the efficiency of this operation really only matters in higher dimensions. I bet a generative model would work, though it's tricky enough for me not to be able to think it through on the spot. Something like: 1. Pick a subset of points thus far generated at random. 2. From this subset, pick the point with the furthest distance from the origin. 3. Form a new unit sphere where r is 1-d of the picked point (ie, make a new sphere that is a subset of the parent sphere with a single touching point of the parent sphere). 4. Generate a new point in this subsphere using the normalized vector method. Not exactly the above, but something like it. The downside of the above approach is that I think it will create a distribution of points that may be unnaturally uniform. It would be interesting to define a set of equations that could benchmark different approaches for how well they compare to the in-cube strategy.