Finding random k points at least d apart in 3D confined space

For my simulation purposes, I want to generate a randomly distributed k number of spheres (having the same radii) in a confined 3D space (inside a rectangle) where k is in order of 1000. Those spheres should not impinge on one another.

So, I want to generate random k points in a 3D space at least d distance away from one another; considering the number of points and the frequency at which I need those points for simulation, I don't want to apply brute force; I'm looking for some efficient algorithms achieving this.