  In the framework of the Standard Model Extension (SME), we present improved
constraints on anisotropic Lorentz invariance and Charge-Parity-Time (CPT)
violation by searching for astrophysical signals of cosmic vacuum birefringence
with broadband optical polarimetry of high redshift astronomical sources,
including Active Galactic Nuclei and Gamma-Ray Burst afterglows. We generalize
the work in Kislat 2018, which studied the SME mass dimension $d = 4$ case, to
arbitrary mass dimension for both the CPT-even and CPT-odd cases. We then
present constraints on all 10, 16, and 42 anisotropic birefringent SME
coefficients for dimension $d = 4$, $d = 5$, and $d = 6$ models, respectively,
using 7554 observations for odd d and 7376 observations for even d of 1278
unique sources on the sky, which, to our knowledge, comprises the most complete
catalog of optical polarization from extragalactic sources in the literature to
date. Compared to the smaller sample of 44 and 45 broadband optical polarimetry
observations analyzed in Kislat 2018 and Kislat and Krawczynski 2017, our
dimension $d = 4$ and $d = 5$ average constraints are more sensitive by factors
of 35 and 10, corresponding to a reduction in allowed SME parameter space
volume for these studies of 15 and 16 orders of magnitude, respectively.
Constraints from individual lines of sight can be significantly stronger using
spectropolarimetry. Nevertheless, due to the increased number of observations
and lines of sight in our catalog, our average $d = 4$ and $d = 5$ broadband
constraints are within factors of 2 and 12 of previous constraints using
spectropolarimetry from Kislat 2018 and Kislat and Krawczynski 2017,
respectively, using an independent data set and an improved analysis method. By
contrast, our anisotropic constraints on all 42 birefringent SME coefficients
for $d = 6$ are the first to be presented in the literature.
