We show that for all 1<k≤logn the k-ary unbiased black-box complexity of the n-dimensional OneMax function class is O(n/k). This indicates that the power of higher arity operators is much stronger than what the previous O(n/logk) bound by Doerr et al. [Benjamin Doerr, Daniel Johannsen, Timo Kötzing, Per Kristian Lehre, Markus Wagner, Carola Winzen, Faster black-box algorithms through higher arity operators, in Proc. of the 11th ACM Workshop on Foundations of Genetic Algorithms, FOGA’11, ACM, 2011, pp. 163–172] suggests. The key to this result is an encoding strategy, which might be of independent interest. It shows that, using k-ary unbiased variation operators only, we may simulate an unrestricted memory of O(2k) bits.