MinT - Best Known (133−62, 133, s)-Nets in Base 9

Best Known (133−62, 133, s)-Nets in Base 9

(133−62, 133, 300)-Net over F₉ — Constructive and digital

Digital (71, 133, 300)-net over F₉, using

1 times m-reduction [i] based on digital (71, 134, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 67, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(133−62, 133, 338)-Net over F₉ — Digital

Digital (71, 133, 338)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−62, 133, 19254)-Net in Base 9 — Upper bound on s

There is no (71, 133, 19255)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 218720 090428 185385 574668 350181 545958 491479 546156 608331 963073 617347 265661 112607 263905 356245 480826 388424 725952 075225 253538 928201 > 9¹³³ [i]