MinT - Best Known (175−54, 175, s)-Nets in Base 3

Best Known (175−54, 175, s)-Nets in Base 3

(175−54, 175, 192)-Net over F₃ — Constructive and digital

Digital (121, 175, 192)-net over F₃, using

3¹ times duplication [i] based on digital (120, 174, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 58, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(175−54, 175, 361)-Net over F₃ — Digital

Digital (121, 175, 361)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−54, 175, 6731)-Net in Base 3 — Upper bound on s

There is no (121, 175, 6732)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 313841 579024 198033 263936 204848 139495 029495 051389 585964 077679 744741 233316 207913 623441 > 3¹⁷⁵ [i]