MinT - Best Known (211−53, 211, s)-Nets in Base 3

Best Known (211−53, 211, s)-Nets in Base 3

(211−53, 211, 288)-Net over F₃ — Constructive and digital

Digital (158, 211, 288)-net over F₃, using

t-expansion [i] based on digital (157, 211, 288)-net over F₃, using
- 8 times m-reduction [i] based on digital (157, 219, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 73, 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]

(211−53, 211, 871)-Net over F₃ — Digital

Digital (158, 211, 871)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−53, 211, 37639)-Net in Base 3 — Upper bound on s

There is no (158, 211, 37640)-net in base 3, because

1 times m-reduction [i] would yield (158, 210, 37640)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15692 634449 532662 466718 166307 973645 921034 561273 827402 309789 264484 158934 140444 461092 497123 183580 850993 > 3²¹⁰ [i]