MinT - Best Known (33−24, 33, s)-Nets in Base 64

Best Known (33−24, 33, s)-Nets in Base 64

(33−24, 33, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 33, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 33, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(33−24, 33, 209)-Net over F₆₄ — Digital

Digital (9, 33, 209)-net over F₆₄, using

net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
  - a curve from the manYPoints database [i]

(33−24, 33, 257)-Net in Base 64 — Constructive

(9, 33, 257)-net in base 64, using

3 times m-reduction [i] based on (9, 36, 257)-net in base 64, using
- base change [i] based on digital (0, 27, 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]

(33−24, 33, 7774)-Net in Base 64 — Upper bound on s

There is no (9, 33, 7775)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 401759 997469 005727 005075 852471 865505 384439 804867 696814 484641 > 64³³ [i]