  We present a detailed discussion of the implementation strategies for a
recently developed $w$-stacking $w$-projection hybrid algorithm used to
reconstruct wide-field interferometric images. In particular, we discuss the
methodology used to deploy the algorithm efficiently on a supercomputer via use
of a Message Passing Interface (MPI) $k$-means clustering technique to achieve
efficient construction and application of non co-planar effects. Additionally,
we show that the use of conjugate symmetry increases the algorithms performance
by imaging an interferometric observation of Fornax A from the Murchison
Widefield Array (MWA). We perform exact non-coplanar wide-field correction for
126.6 million visibilities using 50 nodes of a computing cluster. The
$w$-projection kernel construction takes only 15 minutes, demonstrating that
the implementation is both fast and efficient.
