  We have optimized the parameters of extended relativistic mean-field model
using a selected set of global observables which includes binding energies and
charge radii for nuclei along several isotopic and isotonic chains and the
iso-scalar giant monopole resonance energies for the $^{90}$Zr and $^{208}$Pb
nuclei. The model parameters are further constrained by the available
informations on the energy per neutron for the dilute neutron matter and bounds
on the equations of state of the symmetric and asymmetric nuclear matter at
supra-nuclear densities. Two new parameter sets BSP and IUFSU* are obtained,
later one being the variant of recently proposed IUFSU parameter set. The BSP
parametrization uses the contributions from the quartic order cross-coupling
between $\omega$ and $\sigma$ mesons to model the high density behaviour of the
equation of state instead of the $\omega$ meson self-coupling as in the case of
IUFSU* or IUFSU. Our parameter sets yield appreciable improvements in the
binding energy systematics and the equation of state for the dilute neutron
matter. The importance of the quartic order $\omega-\sigma$ cross coupling term
of the extended RMF model, as often ignored, is realized.
