MinT - Best Known (27, 27+56, s)-Nets in Base 64

Best Known (27, 27+56, s)-Nets in Base 64

(27, 27+56, 177)-Net over F₆₄ — Constructive and digital

Digital (27, 83, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 83, 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]

(27, 27+56, 288)-Net in Base 64 — Constructive

(27, 83, 288)-net in base 64, using

t-expansion [i] based on (22, 83, 288)-net in base 64, using
- 8 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]

(27, 27+56, 425)-Net over F₆₄ — Digital

Digital (27, 83, 425)-net over F₆₄, using

t-expansion [i] based on digital (26, 83, 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]

(27, 27+56, 40508)-Net in Base 64 — Upper bound on s

There is no (27, 83, 40509)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 818506 462406 842940 319344 149085 775041 058946 627057 518642 209718 925756 791738 235560 674721 760816 605156 482328 760734 606637 763175 533226 386699 562477 880755 137203 > 64⁸³ [i]