Let S denote the hypercube $[0, 1]^d$ . What are the best upper and lower bounds you can prove for $n_{pack}(S,ε)$ as a function of ε and d? Justify your bounds with proofs. You may assume that $ ε < 1/d$.
$n_{pack}(S,ε)$ is defined as the maximum set P $\subset$ S [where S is a bounded subset of vector space V] such that for every two distinct vectors x,y $\in$ P, $ ||x-y|| \geq ε$