MinT - Best Known (230−120, 230, s)-Nets in Base 3

Best Known (230−120, 230, s)-Nets in Base 3

(230−120, 230, 74)-Net over F₃ — Constructive and digital

Digital (110, 230, 74)-net over F₃, using

t-expansion [i] based on digital (107, 230, 74)-net over F₃, using
- net from sequence [i] based on digital (107, 73)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(230−120, 230, 104)-Net over F₃ — Digital

Digital (110, 230, 104)-net over F₃, using

t-expansion [i] based on digital (102, 230, 104)-net over F₃, using
- net from sequence [i] based on digital (102, 103)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 102 and N(F) ≥ 104, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(230−120, 230, 724)-Net in Base 3 — Upper bound on s

There is no (110, 230, 725)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 57 150674 971052 565163 326625 138849 728122 522571 495605 120440 344170 857000 538678 446242 670775 730350 254297 412977 297137 > 3²³⁰ [i]