  Context: WISE J085510.83-071442.5 (W0855) is a unique object: with Teff ca.
250 K, it is the coldest known brown dwarf (BD), located at only ca.2.2 pc form
the Sun. It is extremely faint, which makes any astronomical observations
difficult. However, at least one remotely similar ultra-low-mass object, the M9
dwarf TVLM 513-46546, has been shown to be a steady radio emitter at
frequencies up to 95 GHz with superimposed active states where strong, pulsed
emission is observed. Aims: Our goal is to determine the millimeter radio
properties of W0855 with deep observations around 93 GHz (3.2 mm) in order to
investigate whether radio astrometry of this object is feasible and to measure
or set an upper limit on its magnetic field. Methods: We observed W0855 for 94
min at 85.1-100.9 GHz on 24 December 2019 using 44 of the Atacama Large
millimeter Array (ALMA) 12 m antennas. We used the standard ALMA calibration
procedure and created the final image for our analysis by accommodating the
Quasar 3C 209, the brightest nearby object by far. Furthermore, we created a
light curve with a 30 s time resolution to search for pulsed emission. Results:
Our observations achieve a noise RMS of 7.3 {\mu}Jy/beam for steady emission
and of 88 {\mu}Jy for 30 s pulses in the aggregated bandwidth (Stokes I). There
is no evidence for steady or pulsed emission from the object at the time of the
observation. We derive 3 {\sigma} upper limits of 21.9 {\mu}Jy on the steady
emission and of 264 {\mu}Jy on the pulsed emission of W0855 between 85 GHz and
101 GHz. Conclusions: Together with the recent non-detection of W0855 at 4-8
GHz, our constraints on the steady and pulsed emission from W0855 confirm that
the object is neither radio-loud nor magnetospherically particularly active.
