In N-dimensional simplex noise, the squared kernel summation radius $r^2$ is $\frac 1 2$ for all values of N. This is because the edge length of the N-simplex $s = \sqrt {\frac {N} {N + 1}}$ divides out of the N-simplex height $h = s \sqrt {\frac {N + 1} {2N}}$. The kerel summation radius $r$ is equal to the N-simplex height $h$.
$r = h = \sqrt{\frac {1} {2}} = \sqrt{\frac {N} {N+1}} \sqrt{\frac {N+1} {2N}}$