  We study multivariate integration over the $s$-dimensional unit cube in a
weighted space of infinitely differentiable functions. It is known from a
recent result by Suzuki that there exists a good quasi-Monte Carlo (QMC) rule
which achieves a super-polynomial convergence of the worst-case error in this
function space, and moreover, that this convergence behavior is independent of
the dimension under a certain condition on the weights.
  In this paper we provide a constructive approach to finding a good QMC rule
achieving such a dimension-independent super-polynomial convergence of the
worst-case error. Specifically, we prove that interlaced polynomial lattice
rules, with an interlacing factor chosen properly depending on the number of
points $N$ and the weights, can be constructed using a fast
component-by-component algorithm in at most $O(sN(\log N)^2)$ arithmetic
operations to achieve a dimension-independent super-polynomial convergence. The
key idea for the proof of the worst-case error bound is to use a variant of
Jensen's inequality with a purposely-designed concave function.
