  Exoplanets with masses between Earth and Neptune are amongst the most
commonly observed, yet their properties are poorly constrained. Their
transmission spectra are often featureless, which indicate either high-altitude
clouds or a high atmospheric metallicity. The archetypical warm Neptune GJ 436b
is such a planet showing a flat transmission spectrum in observations with the
Hubble Space Telescope (HST). Ground-based high-resolution spectroscopy (HRS)
effectively probes exoplanet atmospheres at higher altitudes and can therefore
be more sensitive to absorption coming from above potential cloud decks. In
this paper we aim to investigate this for the exoplanet GJ 436b. We present new
CRIRES+ HRS transit data of GJ 436b. Three transits were observed, but since
two were during bad weather conditions, only one transit was analyzed. The
radiative transfer code petitRADTRANS was used to create atmospheric models for
cross-correlation and signal-injection purposes, including absorption from
H$_2$O, CH$_4$, and CO. No transmission signals were detected, but atmospheric
constraints can be derived. Injection of artificial transmission signals
indicate that if GJ 436b would have a cloud deck at pressures P>10 mbar and a
<300$\times$ solar metallicity, these CRIRES+ observations should have resulted
in a detection. We estimate that the constraints presented here from one
ground-based HRS transit are slightly better than those obtained with four HST
transits. Combining HRS data from multiple transits is an interesting avenue
for future studies of exoplanets with high-altitude clouds.
