MinT - Best Known (136, 226, s)-Nets in Base 3

Best Known (136, 226, s)-Nets in Base 3

(136, 226, 156)-Net over F₃ — Constructive and digital

Digital (136, 226, 156)-net over F₃, using

2 times m-reduction [i] based on digital (136, 228, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 114, 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]

(136, 226, 210)-Net over F₃ — Digital

Digital (136, 226, 210)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 226, 2150)-Net in Base 3 — Upper bound on s

There is no (136, 226, 2151)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 682697 273870 385894 568800 207331 020114 046522 894462 720340 866490 854232 287999 144981 198685 132762 410653 052718 679735 > 3²²⁶ [i]