Now in the displacement window, engage Smooth Surface and boost your sample count to 70-80,000.

Side note: if this file is to remain in Carrara, doing it this way is a-ok - you might as well use Carrara's dynamic features to enable you to switch tire tread patterns at a moments notice. However, if this is ever to be export into another format, you'll want to definitely want to model the treads to keep polygon counts down. When this object is converted into a mesh instead of a dynamic object, it will have thousands of polygons driving up file size.