MinT - Best Known (129−37, 129, s)-Nets in Base 16

Best Known (129−37, 129, s)-Nets in Base 16

(129−37, 129, 1093)-Net over F₁₆ — Constructive and digital

Digital (92, 129, 1093)-net over F₁₆, using

16¹ times duplication [i] based on digital (91, 128, 1093)-net over F₁₆, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (6, 18, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]
  2. digital (18, 36, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 18, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
  3. digital (37, 74, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 37, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(129−37, 129, 19670)-Net over F₁₆ — Digital

Digital (92, 129, 19670)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−37, 129, large)-Net in Base 16 — Upper bound on s

There is no (92, 129, large)-net in base 16, because

35 times m-reduction [i] would yield (92, 94, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]