MinT - Best Known (17, 17+67, s)-Nets in Base 64

Best Known (17, 17+67, s)-Nets in Base 64

(17, 17+67, 177)-Net over F₆₄ — Constructive and digital

Digital (17, 84, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 84, 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, 17+67, 216)-Net in Base 64 — Constructive

(17, 84, 216)-net in base 64, using

base change [i] based on digital (5, 72, 216)-net over F₁₂₈, using
- net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
    - a function field by SÃ©mirat [i]

(17, 17+67, 267)-Net over F₆₄ — Digital

Digital (17, 84, 267)-net over F₆₄, using

t-expansion [i] based on digital (16, 84, 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, 17+67, 7275)-Net in Base 64 — Upper bound on s

There is no (17, 84, 7276)-net in base 64, because

1 times m-reduction [i] would yield (17, 83, 7276)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 821310 123973 382125 016769 107203 265190 762729 796844 337525 183340 690596 042150 509237 956035 633574 328477 366006 223163 970694 069733 240881 869653 359665 049002 175727 > 64⁸³ [i]