MinT - Best Known (97, 97+140, s)-Nets in Base 3

Best Known (97, 97+140, s)-Nets in Base 3

(97, 97+140, 64)-Net over F₃ — Constructive and digital

Digital (97, 237, 64)-net over F₃, using

t-expansion [i] based on digital (89, 237, 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]

(97, 97+140, 96)-Net over F₃ — Digital

Digital (97, 237, 96)-net over F₃, using

t-expansion [i] based on digital (89, 237, 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]

(97, 97+140, 488)-Net in Base 3 — Upper bound on s

There is no (97, 237, 489)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 125906 693701 085611 877736 451557 255579 966388 127728 179617 861834 926756 996602 222230 867205 002084 206494 659089 623040 512489 > 3²³⁷ [i]