MinT - Best Known (243−97, 243, s)-Nets in Base 3

Best Known (243−97, 243, s)-Nets in Base 3

(243−97, 243, 156)-Net over F₃ — Constructive and digital

Digital (146, 243, 156)-net over F₃, using

5 times m-reduction [i] based on digital (146, 248, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 124, 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]

(243−97, 243, 223)-Net over F₃ — Digital

Digital (146, 243, 223)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−97, 243, 2336)-Net in Base 3 — Upper bound on s

There is no (146, 243, 2337)-net in base 3, because

1 times m-reduction [i] would yield (146, 242, 2337)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 321585 489621 843091 197458 930999 617897 271194 889163 100497 241338 428862 577900 193141 076512 073267 723357 147858 742211 382721 > 3²⁴² [i]