A "wheel set" is not going to accomplish this...if "wheel set" just means different wheels.
To "fill-the-gap" without lowering the car...will require using TIRES that have a taller sidewall than the BMW recommendation. And this will apply to all of the wheel sizes that work (18"/19"/20"/21"/etc). In regards to all of the original wheel/tire recommendations...they all have the same overall rolling diameter (within a small % if any at all)...thus the "gap" from the top of the tire to the bottom of the wheel well opening is the same regardless of the wheel size.
As the wheel gets larger...the aspect ratio of the tire (the middle number) gets lower:
- 18" wheel - 245/45/18 tire
- 19" wheel - 245/40/19 (front) & 275/35/19 (rear) if staggered
- 20" wheel - 245/35/20 (front) & 275/30/20 (rear) if staggered
If you're plan is to "fill-the-gap" without lowering the car...you may want to check/verify if using a tire that has an aspect ratio that is greater than your existing or the BMW recommendation. But again, verify that this will not cause any rubbing of suspension parts.
For example, instead of a 245/45/18 tire...try a 245/50/18 tire. Or instead of a 245/40/19 tire...try a 245/45/19 tire...or instead of a 245/35/20 tire...try a 245/40/20 tire.