The Hubble Space Telescope Cluster Supernova Survey: VI. The Volumetric
  Type Ia Supernova Rate
  We present a measurement of the volumetric Type Ia supernova (SN Ia) rate out
to z ~ 1.6 from the Hubble Space Telescope Cluster Supernova Survey. In
observations spanning 189 orbits with the Advanced Camera for Surveys we
discovered 29 SNe, of which approximately 20 are SNe Ia. Twelve of these SNe Ia
are located in the foregrounds and backgrounds of the clusters targeted in the
survey. Using these new data, we derive the volumetric SN Ia rate in four broad
redshift bins, finding results consistent with previous measurements at z > 1
and strengthening the case for a SN Ia rate that is equal to or greater than
~0.6 x 10^-4/yr/Mpc^3 at z ~ 1 and flattening out at higher redshift. We
provide SN candidates and efficiency calculations in a form that makes it easy
to rebin and combine these results with other measurements for increased
statistics. Finally, we compare the assumptions about host-galaxy dust
extinction used in different high-redshift rate measurements, finding that
different assumptions may induce significant systematic differences between
measurements.
