How to distribute spheres(whose sizes follow a normal distribution) on the surface of a cylinder without overlapping?

I have 150 spheres whose diameters follow a Normal distribution function. There is a cylinder with inner diameter Di, outer diameter Do and length L. The spheres are to be distributed on the surface of the cylinder in a random fashion subjected to the following conditions: 1. The radial location of the centres of the spheres must lie between (Di+Ds(n))/2 (to ensure that spheres do not penetrate the inner dia of the cylinder) and (Do/2)+(4Ds(n)/10)) (to ensure that atleast 10% of the sphere remains inside the outer dia of the cylinder), where Ds(n) is the dia of the nth sphere

2. The radial, angular and axial locations of the grits follow uniform distribution function

3. There is no overlapping of the spheres or at most 5% overlapping I tried and got something like given in the attached file, but still overlapping persisted. I used the condition that distance between the centres of the spheres must be greater than sum of their radii