MinT - Best Known (94, 238, s)-Nets in Base 3

Best Known (94, 238, s)-Nets in Base 3

(94, 238, 64)-Net over F₃ — Constructive and digital

Digital (94, 238, 64)-net over F₃, using

t-expansion [i] based on digital (89, 238, 64)-net over F₃, using
- net from sequence [i] based on digital (89, 63)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(94, 238, 96)-Net over F₃ — Digital

Digital (94, 238, 96)-net over F₃, using

t-expansion [i] based on digital (89, 238, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(94, 238, 454)-Net in Base 3 — Upper bound on s

There is no (94, 238, 455)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 399790 176465 907285 988780 966172 855432 569862 061306 636394 137576 658277 284734 951852 720501 958311 973088 960702 101071 402737 > 3²³⁸ [i]