MinT - Best Known (120−40, 120, s)-Nets in Base 16

Best Known (120−40, 120, s)-Nets in Base 16

(120−40, 120, 1028)-Net over F₁₆ — Constructive and digital

Digital (80, 120, 1028)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (20, 40, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 20, 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]
2. digital (40, 80, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 40, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(120−40, 120, 5223)-Net over F₁₆ — Digital

Digital (80, 120, 5223)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−40, 120, large)-Net in Base 16 — Upper bound on s

There is no (80, 120, large)-net in base 16, because

38 times m-reduction [i] would yield (80, 82, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]