  Understanding the evolution of the superconducting transition temperature in
relation to doping and interaction strengths is one of the most challenging
problems in high temperature superconductivity. By refining determinant quantum
Monte Carlo algorithm, we characterize the parameter dependence of the
superconducting transition temperature within a bilayer Hubbard model, which is
sign-problem-free at arbitrary filling. A striking feature of this model is its
similarities to the bilayer nickelate-based superconductor
$\mathrm{La}_{3}\mathrm{Ni}_{2}\mathrm{O}_{7}$, where superconductivity emerge
from the bilayer $\mathrm{Ni}\mathrm{O}_{2}$ planes. We find that interlayer
spin-exchange $J$ is critical to interlayer pairing, ant that on-site
interaction $U$ contributes negatively to superconductivity at low doping
levels but positively to it at high doping levels. Our findings identify the
key parameter dependent superconducting transition temperature in
nickelate-based superconductors and provide a new understanding of the high
temperature superconductivity.
