MinT - Best Known (238−105, 238, s)-Nets in Base 3

Best Known (238−105, 238, s)-Nets in Base 3

(238−105, 238, 128)-Net over F₃ — Constructive and digital

Digital (133, 238, 128)-net over F₃, using

2 times m-reduction [i] based on digital (133, 240, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 120, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(238−105, 238, 165)-Net over F₃ — Digital

Digital (133, 238, 165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−105, 238, 1460)-Net in Base 3 — Upper bound on s

There is no (133, 238, 1461)-net in base 3, because

1 times m-reduction [i] would yield (133, 237, 1461)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 120321 641615 233297 490541 967795 384251 949766 040864 357520 250662 764429 242713 761117 210601 062955 598684 249191 196374 902033 > 3²³⁷ [i]