A note about weak ε-nets for axis-parallel boxes in d-space

We show the existence of weak ε-nets of size for point sets and axis-parallel boxes in Rd, for d⩾4. Our analysis uses a non-trivial variant of the recent technique of Aronov et al. (2009) [3] that yields (strong) ε-nets, whose size have the above asymptotic bound, for d=2,3.