  New results are presented on a high-statistics measurement of Collins and
Sivers asymmetries of charged hadrons produced in deep inelastic scattering of
muons on a transversely polarised $^6$LiD target. The data were taken in 2022
with the COMPASS spectrometer using the 160 \gevv\ muon beam at CERN, balancing
the existing data on transversely polarised proton targets. The first results
from about two-thirds of the new data have total uncertainties smaller by up to
a factor of three compared to the previous deuteron measurements. Using all the
COMPASS proton and deuteron results, both the transversity and the Sivers
distribution functions of the $u$ and $d$ quark, as well as the tensor charge
in the measured $x$-range are extracted. In particular, the accuracy of the $d$
quark results is significantly improved.
