MinT - Best Known (207−51, 207, s)-Nets in Base 3

Best Known (207−51, 207, s)-Nets in Base 3

(207−51, 207, 328)-Net over F₃ — Constructive and digital

Digital (156, 207, 328)-net over F₃, using

1 times m-reduction [i] based on digital (156, 208, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 52, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(207−51, 207, 926)-Net over F₃ — Digital

Digital (156, 207, 926)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−51, 207, 43434)-Net in Base 3 — Upper bound on s

There is no (156, 207, 43435)-net in base 3, because

1 times m-reduction [i] would yield (156, 206, 43435)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 740718 990761 247613 798853 231128 404310 106451 538023 842259 306912 341415 082692 164015 565700 451218 415207 > 3²⁰⁶ [i]