MinT - Best Known (47, 47+33, s)-Nets in Base 32

Best Known (47, 47+33, s)-Nets in Base 32

(47, 47+33, 273)-Net over F₃₂ — Constructive and digital

Digital (47, 80, 273)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (6, 17, 77)-net over F₃₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (0, 5, 33)-net over F₃₂, using
      - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
        the rational function field F₃₂(x) [i]
        Niederreiter sequence [i]
    2. digital (1, 12, 44)-net over F₃₂, using
      - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
2. digital (7, 23, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
3. digital (7, 40, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(47, 47+33, 515)-Net in Base 32 — Constructive

(47, 80, 515)-net in base 32, using

base change [i] based on digital (17, 50, 515)-net over F₂₅₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 16, 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 (1, 34, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(47, 47+33, 2406)-Net over F₃₂ — Digital

Digital (47, 80, 2406)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+33, 5927266)-Net in Base 32 — Upper bound on s

There is no (47, 80, 5927267)-net in base 32, because

1 times m-reduction [i] would yield (47, 79, 5927267)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 80695 396533 515131 827817 324585 078643 524719 391753 495817 231968 418574 665233 356875 042494 634372 774514 642225 508865 739398 516514 > 32⁷⁹ [i]