we can find an epsilon net with the bound for an epsilon packing

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Corollary

For all $ε > 0$ , there exists an epsilon net $X$ of $B^{d}$ with $| X | \leq {(1 + \frac{2}{ϵ})}^{d}$

Proof

Define $X :=$ any maximal $\frac{ε}{2}$ packing. The result follows from maximal epsilon packing is also a net.

we can find an epsilon net with the bound for an epsilon packing

References

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