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) / \varepsilon\cdot \sqrt{\log 1/\varepsilon ), and we show a near-matching lower bound of size \Omega( d/ \epsilon).