MinT - Best Known (127, 127+42, s)-Nets in Base 3

Best Known (127, 127+42, s)-Nets in Base 3

(127, 127+42, 328)-Net over F₃ — Constructive and digital

Digital (127, 169, 328)-net over F₃, using

3¹ times duplication [i] based on digital (126, 168, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 42, 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]

(127, 127+42, 761)-Net over F₃ — Digital

Digital (127, 169, 761)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+42, 29981)-Net in Base 3 — Upper bound on s

There is no (127, 169, 29982)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 430 120903 380519 002880 452182 666173 485673 342244 351243 529302 675979 513927 435619 016245 > 3¹⁶⁹ [i]