  In General Relativity, there are only two polarizations for gravitational
waves. However, up to six polarizations are possible in a generic metric theory
of gravity. Therefore, measuring the polarization content of gravitational
waves provides an efficient way to test theories of gravity. We analyze the
sensitivity of a next-generation ground-based detector network to nontensorial
polarizations. We present our method to localize GW signals in the
time-frequency domain and construct the model-independent null stream for
events with known sky locations. We obtain results based on simulations of
binary neutron star mergers in a six-detector network. For a single event at a
luminosity distance $D_L=100 \, {\rm Mpc}$, at $5\sigma$ confidence, the
smallest amplitude for detection of scalar and vector modes relative to tensor
modes are respectively $A_{s}=0.045 $ and $A_{v}=0.014 $. For multiple events
in an averaged observing run of 10 years, the detection limits at $5\sigma$
confidence are $A_s=0.05$ and $A_v=0.02$. If we are fortunate, a few strong
events might significantly improve the limits.
