Dual vectors and lower bounds for the nearest lattice point problem

Abstract

We prove that given a point\(\overline z \) outside a given latticeL then there is a dual vector which gives a fairly good estimate for how far from the lattice the vector is. To be more precise, there is a set of translated hyperplanesH i, such thatL⊂∪ iHi andd(\(\overline z \)iHi)≧(6n 2+1)−1 d(\(\overline z \),L).

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Supported by an IBM fellowship.

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Hastad, J. Dual vectors and lower bounds for the nearest lattice point problem. Combinatorica 8, 75–81 (1988). https://doi.org/10.1007/BF02122554

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AMS subject classification (1980)

  • 11 H 60
  • 11 Y 65
  • 68 R 99