Before revision:  Specifically we show a polynomial time construction for a coreset of size O( \sqrt{d\log (1/\epsilon) / \epsilon ), and we show a near-matching lower bound of size \Omega(  d/ \epsilon).
After revision:  Specifically we show a polynomial time construction for a coreset of size O( \sqrt{d\log (1/\epsilon) / \epsilon ), and we show a near-matching lower bound of size \Omega( \min\{ d/ \epsilon).