  Inner-shell electrons naturally sense the electric field close to the
nucleus, which can reach extreme values beyond $10^{15}\,\text{V}/\text{cm}$
for the innermost electrons. Especially in few-electron highly charged ions,
the interaction with the electromagnetic fields can be accurately calculated
within quantum electrodynamics (QED), rendering these ions good candidates to
test the validity of QED in strong fields. Consequently, their Lamb shifts were
intensively studied in the last decades. Another approach is the measurement of
$g$ factors in highly charged ions. However, so far, either experimental
accuracy or small field strength in low-$Z$ ions limited the stringency of
these QED tests. Here, we report on our high-precision, high-field test of QED
in hydrogenlike $^{118}$Sn$^{49+}$. The highly charged ions were produced with
the Heidelberg-EBIT (electron beam ion trap) and injected into the ALPHATRAP
Penning-trap setup, where the bound-electron $g$ factor was measured with a
precision of 0.5 parts-per-billion. For comparison, we present state-of-the-art
theory calculations, which together test the underlying QED to about
$0.012\,\%$, yielding a stringent test in the strong-field regime. With this
measurement, we challenge the best tests via the Lamb shift and, with
anticipated advances in the $g$-factor theory, surpass them by more than an
order of magnitude.
