MinT - Best Known (205−89, 205, s)-Nets in Base 3

Best Known (205−89, 205, s)-Nets in Base 3

(205−89, 205, 128)-Net over F₃ — Constructive and digital

Digital (116, 205, 128)-net over F₃, using

1 times m-reduction [i] based on digital (116, 206, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 103, 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]

(205−89, 205, 152)-Net over F₃ — Digital

Digital (116, 205, 152)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−89, 205, 1363)-Net in Base 3 — Upper bound on s

There is no (116, 205, 1364)-net in base 3, because

1 times m-reduction [i] would yield (116, 204, 1364)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22 128733 829005 916279 186794 063851 988422 611803 601279 834230 271484 068998 133584 327508 205680 839181 532033 > 3²⁰⁴ [i]