MinT - Best Known (230−84, 230, s)-Nets in Base 3

Best Known (230−84, 230, s)-Nets in Base 3

(230−84, 230, 156)-Net over F₃ — Constructive and digital

Digital (146, 230, 156)-net over F₃, using

18 times m-reduction [i] based on digital (146, 248, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 124, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(230−84, 230, 274)-Net over F₃ — Digital

Digital (146, 230, 274)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−84, 230, 3343)-Net in Base 3 — Upper bound on s

There is no (146, 230, 3344)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 777635 975741 304446 979927 278413 891550 703325 825073 746458 000176 882649 020641 756623 975287 947655 056463 441685 794145 > 3²³⁰ [i]