MinT - Best Known (210−87, 210, s)-Nets in Base 3

Best Known (210−87, 210, s)-Nets in Base 3

(210−87, 210, 148)-Net over F₃ — Constructive and digital

Digital (123, 210, 148)-net over F₃, using

2 times m-reduction [i] based on digital (123, 212, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 106, 74)-net over F₉, using
  - net from sequence [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]

(210−87, 210, 177)-Net over F₃ — Digital

Digital (123, 210, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−87, 210, 1717)-Net in Base 3 — Upper bound on s

There is no (123, 210, 1718)-net in base 3, because

1 times m-reduction [i] would yield (123, 209, 1718)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5260 270622 239542 135370 839214 803777 632994 939285 921836 254050 222144 233993 677014 141351 820173 230649 664785 > 3²⁰⁹ [i]