MinT - Best Known (104, 104+57, s)-Nets in Base 3

Best Known (104, 104+57, s)-Nets in Base 3

(104, 104+57, 156)-Net over F₃ — Constructive and digital

Digital (104, 161, 156)-net over F₃, using

3 times m-reduction [i] based on digital (104, 164, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 82, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(104, 104+57, 221)-Net over F₃ — Digital

Digital (104, 161, 221)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 104+57, 2981)-Net in Base 3 — Upper bound on s

There is no (104, 161, 2982)-net in base 3, because

1 times m-reduction [i] would yield (104, 160, 2982)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21984 596835 543121 564300 008502 469214 841080 017772 720616 535868 451803 608016 324601 > 3¹⁶⁰ [i]