MinT - Best Known (128−38, 128, s)-Nets in Base 3

Best Known (128−38, 128, s)-Nets in Base 3

(128−38, 128, 192)-Net over F₃ — Constructive and digital

Digital (90, 128, 192)-net over F₃, using

1 times m-reduction [i] based on digital (90, 129, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 43, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(128−38, 128, 317)-Net over F₃ — Digital

Digital (90, 128, 317)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−38, 128, 6474)-Net in Base 3 — Upper bound on s

There is no (90, 128, 6475)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 790856 643195 814648 705594 702142 274939 730365 566285 572345 632811 > 3¹²⁸ [i]