MinT - Best Known (179−63, 179, s)-Nets in Base 3

Best Known (179−63, 179, s)-Nets in Base 3

(179−63, 179, 156)-Net over F₃ — Constructive and digital

Digital (116, 179, 156)-net over F₃, using

9 times m-reduction [i] based on digital (116, 188, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 94, 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]

(179−63, 179, 245)-Net over F₃ — Digital

Digital (116, 179, 245)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−63, 179, 3378)-Net in Base 3 — Upper bound on s

There is no (116, 179, 3379)-net in base 3, because

1 times m-reduction [i] would yield (116, 178, 3379)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 508865 380934 823326 630419 775071 350716 644279 242969 182454 734200 942040 276414 450802 824851 > 3¹⁷⁸ [i]