MinT - Best Known (237−91, 237, s)-Nets in Base 3

Best Known (237−91, 237, s)-Nets in Base 3

(237−91, 237, 156)-Net over F₃ — Constructive and digital

Digital (146, 237, 156)-net over F₃, using

11 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]

(237−91, 237, 243)-Net over F₃ — Digital

Digital (146, 237, 243)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−91, 237, 2757)-Net in Base 3 — Upper bound on s

There is no (146, 237, 2758)-net in base 3, because

1 times m-reduction [i] would yield (146, 236, 2758)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40369 350995 303394 661844 118840 783866 505248 122577 399249 821746 124911 795829 252216 158492 968402 102139 473609 486430 312981 > 3²³⁶ [i]