MinT - Best Known (27, 27+52, s)-Nets in Base 64

Best Known (27, 27+52, s)-Nets in Base 64

(27, 27+52, 177)-Net over F₆₄ — Constructive and digital

Digital (27, 79, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 79, 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+52, 288)-Net in Base 64 — Constructive

(27, 79, 288)-net in base 64, using

t-expansion [i] based on (22, 79, 288)-net in base 64, using
- 12 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+52, 425)-Net over F₆₄ — Digital

Digital (27, 79, 425)-net over F₆₄, using

t-expansion [i] based on digital (26, 79, 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+52, 51505)-Net in Base 64 — Upper bound on s

There is no (27, 79, 51506)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 48794 292290 745736 855024 342681 952648 717715 807566 048952 678275 697929 690366 544757 300302 919545 999413 721331 866417 160375 547516 260895 994540 665584 536976 > 64⁷⁹ [i]