MinT - Best Known (83−23, 83, s)-Nets in Base 16

Best Known (83−23, 83, s)-Nets in Base 16

(83−23, 83, 1542)-Net over F₁₆ — Constructive and digital

Digital (60, 83, 1542)-net over F₁₆, using

16¹ times duplication [i] based on digital (59, 82, 1542)-net over F₁₆, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 14, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 7, 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 (11, 22, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 11, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)
  3. digital (23, 46, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 23, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(83−23, 83, 21077)-Net over F₁₆ — Digital

Digital (60, 83, 21077)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−23, 83, large)-Net in Base 16 — Upper bound on s

There is no (60, 83, large)-net in base 16, because

21 times m-reduction [i] would yield (60, 62, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]