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.
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