  The vertical diffusive halo size of the Galaxy, $L$, is a key parameter for
dark matter indirect searches. It can be better determined thanks to recent
AMS-02 data. We set constraints on $L$ from Be/B and $^{10}$Be/Be data, and we
performed a consistency check with positron data. We detail the dependence of
Be/B and $^{10}$Be/Be on $L$ and forecast on which energy range better data
would be helpful for future $L$ improvements. We used USINE v3.5 for the
propagation of nuclei, and $e^+$ were calculated with the pinching method of
Boudaud et al. (2017). The current AMS-02 Be/B ($\sim3\%$ precision) and
ACE-CRIS $^{10}$Be/Be ($\sim 10\%$ precision) data bring similar and consistent
constraints on $L$. The AMS-02 Be/B data alone constrain $L=5^{+3}_{-2}$~kpc at
a 68\% confidence level (spanning different benchmark transport
configurations), a range for which most models do not overproduce positrons.
Future experiments need to deliver percent-level accuracy on $^{10}$Be/$^9$Be
anywhere below 10 GV to further constrain $L$. Forthcoming AMS-02, HELIX, and
PAMELA $^{10}$Be/$^9$Be results will further test and possibly tighten the
limits derived here. Elemental ratios involving radioactive species with
different lifetimes (e.g. Al/Mg and Cl/Ar) are also awaited to provide
complementary and robuster constraints.
