MinT - Best Known (129−54, 129, s)-Nets in Base 3

Best Known (129−54, 129, s)-Nets in Base 3

(129−54, 129, 80)-Net over F₃ — Constructive and digital

Digital (75, 129, 80)-net over F₃, using

5 times m-reduction [i] based on digital (75, 134, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 67, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(129−54, 129, 114)-Net over F₃ — Digital

Digital (75, 129, 114)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−54, 129, 1013)-Net in Base 3 — Upper bound on s

There is no (75, 129, 1014)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35 745958 253208 116255 365821 419582 304169 823667 492352 519311 340721 > 3¹²⁹ [i]