MinT - Best Known (9, 39, s)-Nets in Base 64

Best Known (9, 39, s)-Nets in Base 64

(9, 39, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 39, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 39, 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]

(9, 39, 192)-Net in Base 64 — Constructive

(9, 39, 192)-net in base 64, using

3 times m-reduction [i] based on (9, 42, 192)-net in base 64, using
- base change [i] based on digital (3, 36, 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]

(9, 39, 209)-Net over F₆₄ — Digital

Digital (9, 39, 209)-net over F₆₄, using

net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
  - a curve from the manYPoints database [i]

(9, 39, 5056)-Net in Base 64 — Upper bound on s

There is no (9, 39, 5057)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 27625 972045 930833 749923 441766 115108 351112 467796 044270 546011 536843 023808 > 64³⁹ [i]