  Phase shifts for $s$-wave $\pi\pi$ scattering in both the $I=0$ and $I=2$
channels are determined from a lattice QCD calculation performed on 741 gauge
configurations obeying G-parity boundary conditions with a physical pion mass
and lattice size of $32^3\times 64$. These results support our recent study of
direct CP violation in $K\to\pi\pi$ decay~\cite{Abbott:2020hxn}, improving our
earlier 2015 calculation~\cite{Bai:2015nea}. The phase shifts are determined
for both stationary and moving $\pi\pi$ systems, at three ($I=0$) and four
($I=2$) different total momenta. We implement several $\pi\pi$ interpolating
operators including a scalar bilinear "$\sigma$" operator and paired
single-pion bilinear operators with the constituent pions carrying various
relative momenta. Several techniques, including correlated fitting and a
bootstrap determination of p-values have been used to refine the results and a
comparison with the generalized eigenvalue problem (GEVP) method is given. A
detailed systematic error analysis is performed which allows phase shift
results to be presented at a fixed energy.
