Before revision:  The number of stabbing queries performed is O( d^2\log ^{-1 \tldO(d ^9 ^{-1 is the first weak -net related construction where all constants/bounds are polynomial in the dimension.
After revision:  The number of stabbing queries performed is O( d^2\log We present an improved algorithm that computes (roughly) a 1/d^2-centerpoint with running time \tldO(d ^9 ^{-1 is the first weak -net related construction where all constants/bounds are polynomial in the dimension.