  The statistical model with exact conservation of baryon number, electric
charge, and strangeness - the Canonical Statistical Model (CSM) - is used to
analyze the dependence of yields of light nuclei at midrapidity on charged pion
multiplicity at the LHC. The CSM calculations are performed assuming
baryon-symmetric matter, using the recently developed Thermal-FIST package. The
light nuclei-to-proton yield ratios show a monotonic increase with charged pion
multiplicity, with a saturation at the corresponding grand-canonical values in
the high-multiplicity limit, in good qualitative agreement with the
experimental data measured by the ALICE collaboration in pp and Pb-Pb
collisions at different centralities and energies. Comparison with experimental
data at low multiplicities shows that exact conservation of charges across more
than one unit of rapidity and/or a chemical freeze-out temperature which
decreases with the charged pion multiplicity improves agreement with the data.
