How to make sure that a list of generated numbers follow a uniform distribution

I know the title of this question does not help too much, I'm sorry. This is my problem:

I have a list of 150 numbers from 0 to 149. I would like to use a for loop with 150 iterations in order to generate 150 lists of 6 numbers such that,t in each iteration k, the number k is included as well as 5 different random numbers. For example:

S0 = [0, r1, r2, r3, r4, r5] # r1, r2,..., r5 are random numbers between 0 and 150
S1 = [1, r1', r2', r3', r4', r5'] # r1', r2',..., r5' are new random numbers between 0 and 150
...
S149 = [149, r1'', r2'', r3'', r4'', r5''] 

In addition, the numbers in each list have to be different and with a minimum distance of 5. This is the code I am using:

import random
import numpy as np

final_list = []
for k in range(150):
    S = [k]
    for it in range(5):
        domain = [ele for ele in range(150) if ele not in S]
        d = 0
        x = k
        while d < 5:
            d = np.Infinity
            x = random.sample(domain, 1)[0]
            for ch in S:
                if np.abs(ch - x) < d:
                    d = np.abs(ch - x)
        S.append(x)
    final_list.append(S)

Output:

[[0, 149, 32, 52, 39, 126],
 [1, 63, 16, 50, 141, 79],
 [2, 62, 21, 42, 35, 71],
...
 [147, 73, 38, 115, 82, 47],
 [148, 5, 78, 115, 140, 43],
 [149, 36, 3, 15, 99, 23]]

Now, the code is working but I would like to know if it's possible to force that number of repetitions that each number has through all the iterations is approximately the same. For example, after using the previous code, this plot indicates how many times each number has appeared in the generated lists:

As you can see, there are numbers that have appeared more than 10 times while there are others that have appeared only 2 times. Is it possible to reduce this level of variation so that this plot can be approximated as a uniform distribution? Thanks.