Random distribution of N points with a specified average spacing?

This is probably a question of logic more than an algorithm. I want to distribute about N points in such a way that the average distance of a single point to the other N-1 points is uniformly distributed around a value d. That is, The points themselves are not be normally distributed but their spacing with respect to each other is.

Is there a logical way to implement this?

For Example :

X = np.ones(N) #1d for simplicity
d = np.ones(N)

for i in range(N):
    X[i] = ## Insert the algorithm here 
       ##

for i in range(N):
    da = 0 
    for j in range(N):
        if i != j:
            da += np.sqrt(np.abs(X[i]**2 - X[j]**2))  #Calculating distance to other points and 
                                                        summing up
            
    
    da = da / (N-1) # Taking average of all distances
    
    d[i] = da  # the average distance of point i with all other points 

A = np.mean(d) #The mean of all average distances

A is the parameter I want control over. It should be basis for how all the points are distributed.Recommendations using inbuilt Python or C modules would work as well.