suppose we are given the $d$-dimensional hypercube $H^d$ defined as
$$ H^d:=\left\{\sum_{i=1}^d\epsilon_ie_i:\ \epsilon_i\in \{0,1\}\mbox{ for }i=1,\dots , d\right\} $$ and $(e_i)_{i=1}^d$ the standard unit vectors in $\mathbb{R}^d$.
what is the asymptotics of the minimal number of (translates of) balls of radius $r>0$ convering $H^d$?
note that $H^d$ consists only of its vertices.