MinT - Best Known (123−57, 123, s)-Nets in Base 9

Best Known (123−57, 123, s)-Nets in Base 9

(123−57, 123, 300)-Net over F₉ — Constructive and digital

Digital (66, 123, 300)-net over F₉, using

1 times m-reduction [i] based on digital (66, 124, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 62, 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]

(123−57, 123, 324)-Net over F₉ — Digital

Digital (66, 123, 324)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−57, 123, 20291)-Net in Base 9 — Upper bound on s

There is no (66, 123, 20292)-net in base 9, because

1 times m-reduction [i] would yield (66, 122, 20292)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 261 610634 371933 168920 490392 721750 144339 927657 590807 283457 508883 288624 064203 666748 707843 304111 385622 263664 401785 818241 > 9¹²² [i]