MinT - Best Known (90−68, 90, s)-Nets in Base 64

Best Known (90−68, 90, s)-Nets in Base 64

(90−68, 90, 177)-Net over F₆₄ — Constructive and digital

Digital (22, 90, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 90, 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]

(90−68, 90, 288)-Net in Base 64 — Constructive

(22, 90, 288)-net in base 64, using

1 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]

(90−68, 90, 342)-Net over F₆₄ — Digital

Digital (22, 90, 342)-net over F₆₄, using

t-expansion [i] based on digital (20, 90, 342)-net over F₆₄, using
- net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
    - a curve from the manYPoints database [i]

(90−68, 90, 12960)-Net in Base 64 — Upper bound on s

There is no (22, 90, 12961)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 601790 013356 654471 885306 053888 673871 950523 473563 295678 341306 703801 445510 735936 180625 335437 547398 685626 039630 101874 977571 633314 108680 655989 761303 322293 929506 873280 > 64⁹⁰ [i]