MinT - Best Known (230−111, 230, s)-Nets in Base 3

Best Known (230−111, 230, s)-Nets in Base 3

(230−111, 230, 76)-Net over F₃ — Constructive and digital

Digital (119, 230, 76)-net over F₃, using

net from sequence [i] based on digital (119, 75)-sequence over F₃, using
- base reduction for sequences [i] based on digital (22, 75)-sequence over F₉, using
  - s-reduction 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]

(230−111, 230, 125)-Net over F₃ — Digital

Digital (119, 230, 125)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−111, 230, 981)-Net in Base 3 — Upper bound on s

There is no (119, 230, 982)-net in base 3, because

1 times m-reduction [i] would yield (119, 229, 982)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19 163512 224581 564002 088825 529216 038916 307571 323683 852375 151333 071729 599821 732565 918895 884546 792931 568574 889465 > 3²²⁹ [i]