SVP in any finite ℓ_p norm is hard to approximate within 2^{(log n)^{1-o(1)}} via deterministic reduction assuming NP not in subexponential time.
In particular, case (1) enforces that the lattice vector is not only of small norm but also in{−1,0,1} N
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Deterministic Hardness of Approximation For SVP in all Finite $\ell_p$ Norms
SVP in any finite ℓ_p norm is hard to approximate within 2^{(log n)^{1-o(1)}} via deterministic reduction assuming NP not in subexponential time.