MinT - Best Known (183−61, 183, s)-Nets in Base 3

Best Known (183−61, 183, s)-Nets in Base 3

(183−61, 183, 156)-Net over F₃ — Constructive and digital

Digital (122, 183, 156)-net over F₃, using

17 times m-reduction [i] based on digital (122, 200, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 100, 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]

(183−61, 183, 295)-Net over F₃ — Digital

Digital (122, 183, 295)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(183−61, 183, 4694)-Net in Base 3 — Upper bound on s

There is no (122, 183, 4695)-net in base 3, because

1 times m-reduction [i] would yield (122, 182, 4695)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 688 182839 565773 456144 328052 720590 448663 664750 964890 156629 447500 134749 801713 940192 083893 > 3¹⁸² [i]