Recall that \left \{ C_{in}^1, \cdots, C_{in}^N \right \} is a Wozencraft ensemble.
\Delta \left (C_{in}^i \left (c_i^1 \right), C_{in}^i \left (c_i^2 \right ) \right ) \geqslant H_q^{-1} \left (\tfrac{1}{2}-\varepsilon \right ) \cdot 2k.