MinT - Best Known (207−57, 207, s)-Nets in Base 3

Best Known (207−57, 207, s)-Nets in Base 3

(207−57, 207, 288)-Net over F₃ — Constructive and digital

Digital (150, 207, 288)-net over F₃, using

t-expansion [i] based on digital (149, 207, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 69, 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]

(207−57, 207, 609)-Net over F₃ — Digital

Digital (150, 207, 609)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−57, 207, 18262)-Net in Base 3 — Upper bound on s

There is no (150, 207, 18263)-net in base 3, because

1 times m-reduction [i] would yield (150, 206, 18263)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 643869 701045 571989 108860 946180 953458 700470 535308 948838 269789 086020 783601 850369 287751 299727 225033 > 3²⁰⁶ [i]