Let T d : L 2([0, 1] d ) → C([0, 1] d ) be the d-dimensional integration operator. We show that its Kolmogorov and entropy numbers decrease with order at least k −1 (log k) d− 1/2. From this we derive that the small ball probabilities of the Brownian sheet on [0, 1] d under the C([0, 1] d )-norm can be estimated from below by exp(− Cɛ −2¦ log ɛ¦ 2 d−1 ), which improves the best known lower bounds considerably. We also get similar results with respect to certain Orlicz norms.