MinT - Best Known (128−33, 128, s)-Nets in Base 3

Best Known (128−33, 128, s)-Nets in Base 3

(128−33, 128, 264)-Net over F₃ — Constructive and digital

Digital (95, 128, 264)-net over F₃, using

1 times m-reduction [i] based on digital (95, 129, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 43, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(128−33, 128, 533)-Net over F₃ — Digital

Digital (95, 128, 533)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−33, 128, 20813)-Net in Base 3 — Upper bound on s

There is no (95, 128, 20814)-net in base 3, because

1 times m-reduction [i] would yield (95, 127, 20814)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 932966 500761 554042 483895 133441 345936 982296 937381 661616 676769 > 3¹²⁷ [i]