  The paper is devoted to discretization of integral norms of functions from a
given collection of finite dimensional subspaces. For natural collections of
subspaces of the multivariate trigonometric polynomials we construct sets of
points, which are optimally (in the sense of order) good for each subspace of a
collection from the point of view of the integral norm discretization. We call
such sets universal. Our construction of the universal sets is based on deep
results on existence of special nets, known as (t,r,d)-nets.
