MinT - Best Known (227−67, 227, s)-Nets in Base 3

Best Known (227−67, 227, s)-Nets in Base 3

(227−67, 227, 252)-Net over F₃ — Constructive and digital

Digital (160, 227, 252)-net over F₃, using

1 times m-reduction [i] based on digital (160, 228, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 76, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(227−67, 227, 521)-Net over F₃ — Digital

Digital (160, 227, 521)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−67, 227, 12154)-Net in Base 3 — Upper bound on s

There is no (160, 227, 12155)-net in base 3, because

1 times m-reduction [i] would yield (160, 226, 12155)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 676775 142158 366299 146450 581011 579746 678752 399891 018675 382595 345789 799401 029336 172759 768468 067696 632957 523895 > 3²²⁶ [i]