  We study a renormalized coupling g and mass m in four dimensional phi^4
theory on tori with finite size z=mL. Precise numerical values close to the
continuum limit are reported for z=1,2,4, based on Monte Carlo simulations
performed in the equivalent all-order strong coupling reformulation. Ordinary
renormalized perturbation theory is found to work marginally at z=2 and and to
fail at z=1. By exactly integrating over the constant field mode we set up a
renormalized expansion in z and compute three nontrivial orders. These results
reasonably agree with the numerical data at small z. In the new expansion, the
universal continuum limit exists as expected from multiplicative
renormalizability. The triviality scenario is corroborated with significant
precision.
