Before revision:  We show that in this setting one can construct (k,\eps) -nets of size m = (1/ ^{1-k/d), where } hides polylogarithmic factors. That is , there is a set of m k-flats, such that any convex body in [0,1]^d of volume larger than \eps is stabbed by one of these k-flats.
After revision:  We show that in this setting one can construct (k,\eps) -nets of size m = (1/ ^{1-k/d), where } -net is a set of m k-flats, such that any convex body in [0,1]^d of volume larger than \eps is stabbed by one of these k-flats.