  We prove that given any set of $n$ unit vectors $\{v_i\}_{i=1}^{n}\subset
\mathbb R^n,$ the inequality \[ \sup\limits_{\Vert x \Vert_{\mathbb R^n} =1}
\vert \langle x, v_1 \rangle \cdots \langle x, v_n\rangle\vert \ge n^{-n/2} \]
holds for $n \le 14.$ Moreover, the equality is attained if and only if
$\{v_i\}_{i=1}^{n}$ is an orthonormal system.
