We prove the “net theorem” discussed in my previous talk in the Probability seminar. The “lite version” of the theorem states the existence of a net around the sphere of cardinality 100^n, such that for every random matrix A with independent columns, with probability 1-5^{-n}, the values of |Ax| on the sphere can be compared to its values on the net. The error in this comparison is optimal, and the formulation of the theorem is scale-invariant. We emphasize that the only assumption required for this is the independence of columns. The proof consists of four steps, and shall be outlined.