  We construct the equation of state (EOS) of dense matter covering a wide
range of temperature, proton fraction, and density for the use of core-collapse
supernova simulations. The study is based on the relativistic mean-field (RMF)
theory, which can provide an excellent description of nuclear matter and finite
nuclei. The Thomas--Fermi approximation in combination with assumed nucleon
distribution functions and a free energy minimization is adopted to describe
the non-uniform matter, which is composed of a lattice of heavy nuclei. We
treat the uniform matter and non-uniform matter consistently using the same RMF
theory. We present two sets of EOS tables, namely EOS2 and EOS3. EOS2 is an
update of our earlier work published in 1998 (EOS1), where only the nucleon
degree of freedom is taken into account. EOS3 includes additional contributions
from $\Lambda$ hyperons. The effect of $\Lambda$ hyperons on the EOS is
negligible in the low-temperature and low-density region, whereas it tends to
soften the EOS at high density. In comparison with EOS1, EOS2 and EOS3 have an
improved design of ranges and grids, which covers the temperature range
$T=0.1$--$10^{2.6}$ MeV with the logarithmic grid spacing $\Delta
\log_{10}(T/\rm{[MeV]})=0.04$ (92 points including T=0), the proton fraction
range $Y_p=0$--0.65 with the linear grid spacing $\Delta Y_p = 0.01$ (66
points), and the density range $\rho_B=10^{5.1}$--$10^{16}\,\rm{g\,cm^{-3}}$
with the logarithmic grid spacing $\Delta \log_{10}(\rho_B/\rm{[g\,cm^{-3}]}) =
0.1$ (110 points).
