MinT - Best Known (232−128, 232, s)-Nets in Base 3

Best Known (232−128, 232, s)-Nets in Base 3

(232−128, 232, 71)-Net over F₃ — Constructive and digital

Digital (104, 232, 71)-net over F₃, using

net from sequence [i] based on digital (104, 70)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 70)-sequence over F₉, using
  - s-reduction 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]

(232−128, 232, 104)-Net over F₃ — Digital

Digital (104, 232, 104)-net over F₃, using

t-expansion [i] based on digital (102, 232, 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]

(232−128, 232, 600)-Net in Base 3 — Upper bound on s

There is no (104, 232, 601)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 502 511418 631001 458626 910757 242627 415822 220540 153651 924243 202527 026514 315135 017578 142044 922785 825386 034167 504129 > 3²³² [i]