MinT - Best Known (233−140, 233, s)-Nets in Base 3

Best Known (233−140, 233, s)-Nets in Base 3

(233−140, 233, 64)-Net over F₃ — Constructive and digital

Digital (93, 233, 64)-net over F₃, using

t-expansion [i] based on digital (89, 233, 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]

(233−140, 233, 96)-Net over F₃ — Digital

Digital (93, 233, 96)-net over F₃, using

t-expansion [i] based on digital (89, 233, 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]

(233−140, 233, 455)-Net in Base 3 — Upper bound on s

There is no (93, 233, 456)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1679 201864 413020 846874 056087 522383 772666 235685 537903 184156 810602 181803 832049 692159 495125 951300 888430 049789 159089 > 3²³³ [i]