Before revision:  In this paper, we strengthen the above result and show that using a careful chaining argument, the error probability can be reduced to \delta^{1-c}  \exp(c'n^{1/3+c}) for arbitrarily small constants c>0 and some constant c'>0.
After revision:  In this paper, we strengthen the above result and show that using a careful chaining argument, the error probability can be reduced to \delta^{1-c} \cdot \exp(c'n^{1/3+c}) for arbitrarily small constants c>0 and some constant c'>0.