This is a nitpick but also it's been a few years since I was taking academic ML and linear algebra courses. However regarding this part.

> So you only gain a factor 2 * L. But the trade-off is that you are doing a near neighbor search in higher dimension where you are then subjected to the curse of dimensionality (the higher the dimension the more similar all points are to each other).

I thought that the curse of dimensionality meant that in higher dimension, points got farther apart