The reason for shooting at minimum aperture is to reduce the size of the strong light source as much as possible. Usually that means you get "ray bursts" around say the sun, which we intuitively see as "true", perhaps subconsciously reminding of how we in childhood drew the sun (circle with rays coming from it).
The smallest size of say the bright sun will be provided by a lens with short focal length, because the size of the blur circles is proportional to absolute aperture (and accordingly, diminishes for a short focal length *and* aperture setting). Fisheye lenses are favourites because by definition most light entering such optics will be image-forming not stray light. This assumes an immaculately clean front element though.
Although longer lenses yield larger blur circles, one can still get nice light "burst" provided the light source is small enough, or effectively is blocked so only part of its light reaches the camera.
The attached images show some of these features. First, two old shots with a fast lens (Noct) at f/16. The lens does perform pretty well even for shooting into the sun, but some irregularities are evident, likely caused by dust on front. The solar disc is rendered more like a blob and ray bursts are not very evident. In the second picture, the sun is partially blocked by foliage, its disc is smaller, and now ray bursts show better.
Finally, a winter scene by the even longer 105/2.5 Nikkor AI. When the sun is blocked more efficiently like here, even better ray bursts are attainable.
