Correlated enhancement of H$_{c2}$ and J$_{c}$ in carbon nanotube-doped MgB$_{2}$.

We achieved simultaneous enhancement of upper critical magnetic field, H$_{c2}$, and critical current density, J$_{c}$, by doping polycrystalline samples of MgB$_{2}$ with double-wall carbon nanotubes (DWCNT), a source of atomic carbon. The optimum DWCNT content from the point of view of the J$_{c}$ is in the range 2.5-10{\%} at depending on field and temperature. Record values for H$_{c2}$ (4K) = 41.9 T (with extrapolated H$_{c2}$(0) $\approx $ 44.4 T) are reached in a bulk sample with 10{\%} at DWCNT content. The measured H$_{c2}$ vs T in all samples are successfully~described using a theoretical model for a two-gap superconductor in the dirty limit first proposed by Gurevich \textit{et al}.