  In this paper, we relate the problem of generating all 2-level orthogonal
arrays of given dimension and force, i.e. elements in OA$(n,m)$, where $n$ is
the number of factors and $m$ the force, to the solution of an Integer
Programming problem involving rational convex cones. We do not restrict the
number of points in the array, i.e. we admit any number of replications. This
problem can be theoretically solved by means of Hilbert bases which form a
finite generating set for all the elements in in the infinite set OA$(n,m)$. We
discuss some examples which are explicitly solved with a software performing
Hilbert bases computation.
