MinT - Best Known (170−43, 170, s)-Nets in Base 3

Best Known (170−43, 170, s)-Nets in Base 3

(170−43, 170, 288)-Net over F₃ — Constructive and digital

Digital (127, 170, 288)-net over F₃, using

4 times m-reduction [i] based on digital (127, 174, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 58, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(170−43, 170, 712)-Net over F₃ — Digital

Digital (127, 170, 712)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−43, 170, 29981)-Net in Base 3 — Upper bound on s

There is no (127, 170, 29982)-net in base 3, because

1 times m-reduction [i] would yield (127, 169, 29982)-net in base 3, but
- 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]