MinT - Best Known (236−93, 236, s)-Nets in Base 3

Best Known (236−93, 236, s)-Nets in Base 3

(236−93, 236, 156)-Net over F₃ — Constructive and digital

Digital (143, 236, 156)-net over F₃, using

6 times m-reduction [i] based on digital (143, 242, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 121, 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]

(236−93, 236, 225)-Net over F₃ — Digital

Digital (143, 236, 225)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−93, 236, 2418)-Net in Base 3 — Upper bound on s

There is no (143, 236, 2419)-net in base 3, because

1 times m-reduction [i] would yield (143, 235, 2419)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13289 912818 590967 552393 864558 070017 750839 684794 586080 727345 865707 335955 325165 725782 460757 581914 006840 608329 768045 > 3²³⁵ [i]