MinT - Best Known (76−28, 76, s)-Nets in Base 16

Best Known (76−28, 76, s)-Nets in Base 16

(76−28, 76, 579)-Net over F₁₆ — Constructive and digital

Digital (48, 76, 579)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (6, 20, 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 (28, 56, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 28, 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]

(76−28, 76, 1799)-Net over F₁₆ — Digital

Digital (48, 76, 1799)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(76−28, 76, 1386805)-Net in Base 16 — Upper bound on s

There is no (48, 76, 1386806)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 32 592812 008608 182767 113551 729625 945970 345998 918096 522150 016659 562497 936968 275097 388350 697736 > 16⁷⁶ [i]