MinT - Best Known (84−39, 84, s)-Nets in Base 8

Best Known (84−39, 84, s)-Nets in Base 8

(84−39, 84, 208)-Net over F₈ — Constructive and digital

Digital (45, 84, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 42, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(84−39, 84, 226)-Net over F₈ — Digital

Digital (45, 84, 226)-net over F₈, using

trace code for nets [i] based on digital (3, 42, 113)-net over F₆₄, using
- net from sequence [i] based on digital (3, 112)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
    - a curve from the manYPoints database [i]

(84−39, 84, 9969)-Net in Base 8 — Upper bound on s

There is no (45, 84, 9970)-net in base 8, because

1 times m-reduction [i] would yield (45, 83, 9970)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 905 028265 214651 921892 254040 360248 787592 529183 431495 482237 599620 420511 061680 > 8⁸³ [i]