Theorem

Assume the source pdf satisfies $\int\limits _{-\infty}^{\infty}|x|^{2+\epsilon}f(x) \, dx<\infty$ for some $\epsilon>0$. Then $$\lim_{ N \to \infty } N^{2}D^{*}(N)=\frac{1}{12}\|f\|_{\frac{1}{3}}$$ or by Hölder’s Inequality $$D^{*}(N)=\min_{G}D(Q_{G,N})\approx \frac{1}{12N^{2}}\|f\|_{\frac{1}{3}}$$