  We report a density-matrix renormalization group study of the lightly doped
$t$-$J$ model on a 4-leg cylinder with doped hole concentrations per site
$\delta=5\%\sim 12.5\%$. By keeping an unusually large number of states and
long system sizes, we are able to accurately document the interplay between
d-wave superconductivity (SC) and spin and charge-density-wave (CDW) orders.
The long-distance behavior is consistent with that of a Luther-Emery liquid
with a spin-gap, power-law CDW correlations with wave-length $\lambda
=1/2\delta$, and power-law SC correlations. This is the widest (most nearly 2D)
such system for which power law SC correlations have been established.
