MinT - Best Known (171−43, 171, s)-Nets in Base 3

Best Known (171−43, 171, s)-Nets in Base 3

(171−43, 171, 288)-Net over F₃ — Constructive and digital

Digital (128, 171, 288)-net over F₃, using

t-expansion [i] based on digital (127, 171, 288)-net over F₃, using
- 3 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]

(171−43, 171, 732)-Net over F₃ — Digital

Digital (128, 171, 732)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−43, 171, 31593)-Net in Base 3 — Upper bound on s

There is no (128, 171, 31594)-net in base 3, because

1 times m-reduction [i] would yield (128, 170, 31594)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1290 913264 086461 847802 595223 287351 964036 310965 963697 424623 622429 980802 169871 839117 > 3¹⁷⁰ [i]