Let T_d : L₂([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(-Cε^-2|log ε|^2d-1), which improves the best known lower bounds considerably. We also get similar results with respect to certain Orlicz norms.