MinT - Best Known (117−57, 117, s)-Nets in Base 9

Best Known (117−57, 117, s)-Nets in Base 9

(117−57, 117, 200)-Net over F₉ — Constructive and digital

Digital (60, 117, 200)-net over F₉, using

1 times m-reduction [i] based on digital (60, 118, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 59, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(117−57, 117, 252)-Net over F₉ — Digital

Digital (60, 117, 252)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−57, 117, 12665)-Net in Base 9 — Upper bound on s

There is no (60, 117, 12666)-net in base 9, because

1 times m-reduction [i] would yield (60, 116, 12666)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 492 706306 164216 258178 139649 247204 956024 854474 601613 543855 251481 304134 076886 672015 706767 696745 240660 446057 243713 > 9¹¹⁶ [i]