Before revision:  In  case that k is known in the preprocessing stage \eps we propose a fully deterministic data structure whose space is O(n ( 32d\big(\big\{\big(}{\eps}}\big)
After revision:  In case that k is known in the preprocessing stage \eps we propose a fully deterministic data structure whose space is O(n ( 32d\big(\big\{\big(\frac{\sqrt{d}{\eps}}\big)