Before revision:  (B) If one is allowed to expand the convex range before checking if it intersects the sample, then a sample of size ( ^{-(d+1)/2), from the original point set, is sufficient to form a net.
After revision:  (B) If one is allowed to expand the convex range before checking if it intersects the sample, then a sample of size ( ), from the original point set, is sufficient to form a net.