# Random placement of euclidean points with constrained inter-point distances in a fixed area

I'd like to place as many random points as possible in a 2D square $S=[0,1]x[0,1]$ such that the euclidean distance $d$ between any two points $d$ is greater than a given value $b$ (b is small). I'm interested in an iterative construction algorithm that successively limits the remaining space where points can be placed. In such a case, I'm curious how to efficiently characterize the available space and how to check the stopping criteria "until no more points can be placed". Any help would be greatly appreciated.