MinT - Best Known (237−63, 237, s)-Nets in Base 3

Best Known (237−63, 237, s)-Nets in Base 3

(237−63, 237, 288)-Net over F₃ — Constructive and digital

Digital (174, 237, 288)-net over F₃, using

t-expansion [i] based on digital (173, 237, 288)-net over F₃, using
- 6 times m-reduction [i] based on digital (173, 243, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 81, 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]

(237−63, 237, 776)-Net over F₃ — Digital

Digital (174, 237, 776)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−63, 237, 26593)-Net in Base 3 — Upper bound on s

There is no (174, 237, 26594)-net in base 3, because

1 times m-reduction [i] would yield (174, 236, 26594)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 39868 142055 009106 690155 760232 993558 243366 783150 536578 076249 609088 114707 368297 776852 780823 049427 626028 173965 187449 > 3²³⁶ [i]