MinT - Best Known (26, 26+46, s)-Nets in Base 64

Best Known (26, 26+46, s)-Nets in Base 64

(26, 26+46, 177)-Net over F₆₄ — Constructive and digital

Digital (26, 72, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 72, 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]

(26, 26+46, 288)-Net in Base 64 — Constructive

(26, 72, 288)-net in base 64, using

t-expansion [i] based on (22, 72, 288)-net in base 64, using
- 19 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
  - base change [i] based on digital (9, 78, 288)-net over F₁₂₈, using
    - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(26, 26+46, 425)-Net over F₆₄ — Digital

Digital (26, 72, 425)-net over F₆₄, using

net from sequence [i] based on digital (26, 424)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 26 and N(F) ≥ 425, using
  - a curve from the manYPoints database [i]

(26, 26+46, 513)-Net in Base 64

(26, 72, 513)-net in base 64, using

base change [i] based on digital (8, 54, 513)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 512)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(26, 26+46, 67479)-Net in Base 64 — Upper bound on s

There is no (26, 72, 67480)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 11092 949448 217189 664418 843942 088364 353542 088122 320717 201062 464538 375110 327888 049573 836872 041770 332255 547774 088299 150014 116236 185911 > 64⁷² [i]