MinT - Best Known (74, 117, s)-Nets in Base 9

Best Known (74, 117, s)-Nets in Base 9

(74, 117, 448)-Net over F₉ — Constructive and digital

Digital (74, 117, 448)-net over F₉, using

5 times m-reduction [i] based on digital (74, 122, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 61, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(74, 117, 961)-Net over F₉ — Digital

Digital (74, 117, 961)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 117, 202502)-Net in Base 9 — Upper bound on s

There is no (74, 117, 202503)-net in base 9, because

1 times m-reduction [i] would yield (74, 116, 202503)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 492 237927 902964 679389 147274 479942 524326 702481 267315 382528 115731 428280 056452 242424 349693 863530 129256 637515 172505 > 9¹¹⁶ [i]