Efficient way to sample N points from a 3D space with the constraint of a minimum distance between two points in Python

I have 200 data points, each point is a list of 3 numbers that represents the position. I want to sample N=100 points from this 3D space, but with the constraint that the minimum distance between every two points must be larger than 0.15. The script below is the way I sample the points, but it just keeps running and never stops. Also, if I set a N larger than a value, the code cannot find all N points because I sample each point randomly and it gets to a point where no points can be sampled that isn't too close to the current points, but in reality the N can be much larger than this value if the point distribution is very "dense" (but still satisfies minimum distance larger than 0.15). Is there a more efficient way to do this?

import numpy as np
import random
import time

def get_random_points_not_too_close(points, npoints, min_distance):
    random.shuffle(points)
    final_points = [points[0]]
    while len(final_points) < npoints:
        for point in points:
            if point in final_points:
                pass
            elif min([np.linalg.norm(np.array(p) - np.array(point)) for p in final_points]) > min_distance:
                final_points.append(point)

    return final_points


data = [[random.random() for i in range(3)] for j in range(200)]
t1 = time.time()
sample_points = get_random_points_not_too_close(points=data, npoints=100, min_distance=0.15)
t2 = time.time()
print(t2-t1)