high dan

A high dan, depending on your perspective, in the world of Go amateurs would be a 4 dan or 5 dan up to 6 dan and 7 dan.

A low dan, likewise, would be a 1 dan and 2 dan up to a 3 dan or 4 dan.

In the world of professionals, there is less of a distinction between high and low dans. The difference in strength is not one stone per grade, and moreover high dan grades can be historically built or granted by committee but no longer reflecting real strength. See A One-Dan Pro may be Stronger than a Nine-Dan Pro.