MinT - Best Known (210−89, 210, s)-Nets in Base 3

Best Known (210−89, 210, s)-Nets in Base 3

(210−89, 210, 128)-Net over F₃ — Constructive and digital

Digital (121, 210, 128)-net over F₃, using

6 times m-reduction [i] based on digital (121, 216, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 108, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(210−89, 210, 166)-Net over F₃ — Digital

Digital (121, 210, 166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−89, 210, 1549)-Net in Base 3 — Upper bound on s

There is no (121, 210, 1550)-net in base 3, because

1 times m-reduction [i] would yield (121, 209, 1550)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5228 222855 854597 239128 814899 787184 536088 144125 729421 174571 481696 147898 369884 647262 274957 839615 050265 > 3²⁰⁹ [i]