MinT - Best Known (210−82, 210, s)-Nets in Base 3

Best Known (210−82, 210, s)-Nets in Base 3

(210−82, 210, 156)-Net over F₃ — Constructive and digital

Digital (128, 210, 156)-net over F₃, using

2 times m-reduction [i] based on digital (128, 212, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 106, 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]

(210−82, 210, 209)-Net over F₃ — Digital

Digital (128, 210, 209)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−82, 210, 2202)-Net in Base 3 — Upper bound on s

There is no (128, 210, 2203)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15972 427354 667223 527980 923765 406280 573223 718587 435147 405717 241294 533734 820599 345345 458000 375260 596391 > 3²¹⁰ [i]