  Many of the currently available equations of state for core-collapse
supernova simulations give large neutron star radii and do not provide large
enough neutron star masses, both of which are inconsistent with some recent
neutron star observations. In addition, one of the critical uncertainties in
the nucleon-nucleon interaction, the nuclear symmetry energy, is not fully
explored by the currently available equations of state. In this article, we
construct two new equations of state which match recent neutron star
observations and provide more flexibility in studying the dependence on nuclear
matter properties. The equations of state are also provided in tabular form,
covering a wide range in density, temperature and asymmetry, suitable for
astrophysical simulations. These new equations of state are implemented into
our spherically symmetric core-collapse supernova model, which is based on
general relativistic radiation hydrodynamics with three-flavor Boltzmann
neutrino transport. The results are compared with commonly used equations of
state in supernova simulations of 15 and 40 solar mass progenitors. We do not
find any simple correlations between individual nuclear matter properties at
saturation and the outcome of these simulations. However, the new equations of
state lead to the most compact neutron stars among the relativistic mean-field
models which we considered. The new models also obey the previously observed
correlation between the time to black hole formation and the maximum mass of an
s=4 neutron star.
