MinT - Best Known (17, 90, s)-Nets in Base 64

Best Known (17, 90, s)-Nets in Base 64

(17, 90, 177)-Net over F₆₄ — Constructive and digital

Digital (17, 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]

(17, 90, 192)-Net in Base 64 — Constructive

(17, 90, 192)-net in base 64, using

t-expansion [i] based on (16, 90, 192)-net in base 64, using
- 1 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
  - base change [i] based on digital (3, 78, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(17, 90, 267)-Net over F₆₄ — Digital

Digital (17, 90, 267)-net over F₆₄, using

t-expansion [i] based on digital (16, 90, 267)-net over F₆₄, using
- net from sequence [i] based on digital (16, 266)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 16 and N(F) ≥ 267, using
    - a curve from the manYPoints database [i]

(17, 90, 6599)-Net in Base 64 — Upper bound on s

There is no (17, 90, 6600)-net in base 64, because

1 times m-reduction [i] would yield (17, 89, 6600)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56498 114737 518041 920771 394569 894248 459119 656445 748820 832131 786541 532065 202617 750871 934348 804648 467010 690778 934733 164233 948896 557333 159006 331685 252544 023333 525278 > 64⁸⁹ [i]