  In their GECCO'12 paper, Doerr and Doerr proved that the $k$-ary unbiased
black-box complexity of OneMax on $n$ bits is $O(n/k)$ for $2\le k\le O(\log
n)$. We propose an alternative strategy for achieving this unbiased black-box
complexity when $3\le k\le\log_2 n$. While it is based on the same idea of
block-wise optimization, it uses $k$-ary unbiased operators in a different way.
  For each block of size $2^{k-1}-1$ we set up, in $O(k)$ queries, a virtual
coordinate system, which enables us to use an arbitrary unrestricted algorithm
to optimize this block. This is possible because this coordinate system
introduces a bijection between unrestricted queries and a subset of $k$-ary
unbiased operators. We note that this technique does not depend on OneMax being
solved and can be used in more general contexts.
  This together constitutes an algorithm which is conceptually simpler than the
one by Doerr and Doerr, and at the same time achieves better constant factors
in the asymptotic notation. Our algorithm works in $(2+o(1))\cdot n/(k-1)$,
where $o(1)$ relates to $k$. Our experimental evaluation of this algorithm
shows its efficiency already for $3\le k\le6$.
