\begin{block}{Summary}
\begin{itemize}
\item Goal: description of a method to compute a large class of truly
  chaotic PRNGs
\item The chaotic iterated map inside the generator: built by removing 
from a $n$-cube an Hamiltonian path, \textit{i.e.}, a balanced Gray code
\item Statistical properties: established for $n=4,5,6,7,8$  through
NIST and DieHARD batteries
\end{itemize}
\end{block}

\begin{block}{Open Problems}
\begin{itemize}
\item Our proposal: remove from the $n$-cube an Hamiltonian path that 
is a  balanced Gray code. \alert{Can we prove that this solution is the one that
  minimizes the  mixing time?}
\item Lack of constructive method to built balanced Gray Code
with large $n$. \alert{Can we propose a new algorithm?}
\end{itemize}
\end{block}