Obviously, the number of iterations $b$ has to be sufficiently large
to provide a uniform output distribution.
To reduce the number of iterations, the provided Gray code
-should ideally possess the both balanced and locally balanced properties.
+should ideally possess both balanced and locally balanced properties.
However, none of the two algorithms is compatible with the second one:
balanced Gray codes that are generated by state of the art works~\cite{ZanSup04,DBLP:journals/combinatorics/BhatS96} are not locally balanced. Conversely,
locally balanced Gray codes yielded by Igor Bykov approach~\cite{Bykov2016}
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