MinT - Best Known (211−91, 211, s)-Nets in Base 3

Best Known (211−91, 211, s)-Nets in Base 3

(211−91, 211, 128)-Net over F₃ — Constructive and digital

Digital (120, 211, 128)-net over F₃, using

3 times m-reduction [i] based on digital (120, 214, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 107, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(211−91, 211, 159)-Net over F₃ — Digital

Digital (120, 211, 159)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−91, 211, 1440)-Net in Base 3 — Upper bound on s

There is no (120, 211, 1441)-net in base 3, because

1 times m-reduction [i] would yield (120, 210, 1441)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15689 320008 885576 625644 032590 111493 027638 228025 119614 778748 556197 522887 900630 210857 457045 321266 269331 > 3²¹⁰ [i]