I don't know of defined minimum, however there are common sense issues here. Consider what is achieved in terms of stress re-distrbution by adding a ring and altering the local flexibility of the connection.

A very small ring will not add any stiffness, and welds that are too close may make the situation worse.

Since the maximum size allowed to be considered for pressure ... although a ring could actually be larger diameter ... is clearly defined, I would aim for that figure. Then you can be confident that you will be in the geometry regime to which B31.3 pp D SIF's apply.