MinT - Best Known (236−91, 236, s)-Nets in Base 3

Best Known (236−91, 236, s)-Nets in Base 3

(236−91, 236, 156)-Net over F₃ — Constructive and digital

Digital (145, 236, 156)-net over F₃, using

10 times m-reduction [i] based on digital (145, 246, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 123, 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]

(236−91, 236, 240)-Net over F₃ — Digital

Digital (145, 236, 240)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−91, 236, 2689)-Net in Base 3 — Upper bound on s

There is no (145, 236, 2690)-net in base 3, because

1 times m-reduction [i] would yield (145, 235, 2690)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13362 980731 199789 270819 601175 071932 548514 593625 055149 511140 331275 365236 639181 238605 428500 652792 881741 649674 900493 > 3²³⁵ [i]