MinT - Best Known (234−63, 234, s)-Nets in Base 3

Best Known (234−63, 234, s)-Nets in Base 3

(234−63, 234, 288)-Net over F₃ — Constructive and digital

Digital (171, 234, 288)-net over F₃, using

6 times m-reduction [i] based on digital (171, 240, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 80, 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]

(234−63, 234, 733)-Net over F₃ — Digital

Digital (171, 234, 733)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−63, 234, 23908)-Net in Base 3 — Upper bound on s

There is no (171, 234, 23909)-net in base 3, because

1 times m-reduction [i] would yield (171, 233, 23909)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1477 291882 416773 917291 573019 455369 803825 546965 512886 239736 948882 502939 224659 468339 888048 225459 283957 136036 829755 > 3²³³ [i]