  The origin of a high Neel temperature in a 5$d$ oxide, NaOsO$_3$, has been
analyzed within the mean-field limit of a multiband Hubbard model and compared
with the analogous 4$d$ oxide, SrTcO$_3$. Our analysis shows that there are a
lot of similarities in both these oxides on the dependence of the the effective
exchange interaction strength ($J_0$) on the electron-electron interaction
strength ($U$). However, the relevant value of $U$ in each system puts them in
different portions of the parameter space. Although the Neel temperature for
NaOsO$_3$ is less than that for SrTcO$_3$, our results suggest that there could
be examples among other 5$d$ oxides which have a higher Neel temperature. We
have also examined the stability of the G-type antiferromagnetic state found in
NaOsO$_3$ as a function of electron doping within GGA+U calculations and find a
robust G-type antiferromagnetic metallic state stabilized. The most surprising
aspect of the doped results is the rigid band-like evolution of the electronic
structure which indicates that the magnetism in NaOsO$_3$ is not driven by
fermi surface nesting.
