I'm wondering if formulas exist for the radius and amplitude of the hypersphere kernel used in Simplex noise, generalized to an arbitrary number of dimensions. Ideally I'd like an answer with two equations in terms of n (number of dimensions) that give me r (radius) and a (amplitude), as well as an explanation of what makes these formulas significant.
Here is a link to a document descrbing the Simplex noise algorithm. It mentions that the radius and amplitude need to be tuned, but it doesn't specify what values to use, like they're just fudge factors.