  We present the measurements of individual bound electron $g$ factors of
$^{20}\text{Ne}^{9+}$ and $^{22}\text{Ne}^{9+}$ on the relative level of
$0.1\,\text{parts}$ per billion. The comparison with theory represents the most
stringent test of bound-state QED in strong electric fields. A dedicated mass
measurement results in
$m\left(^{20}\text{Ne}\right)=19.992\,440\,168\,77\,(9)\,\text{u}$, which
improves the current literature value by a factor of nineteen, disagrees by $4$
standard deviations and represents the most precisely measured mass value in
atomic mass units. Together, these measurements yield an electron mass on the
relative level of $0.1\,\text{ppb}$ with
$m_{\text{e}}=5.485\,799\,090\,99\,(59) \times 10^{-4}\,\text{u}$ as well as a
factor of eight improved
$m\left(^{22}\text{Ne}\right)=21.991\,385\,098\,2\,(26)\,\text{u}$.
