MinT - Best Known (218−86, 218, s)-Nets in Base 3

Best Known (218−86, 218, s)-Nets in Base 3

(218−86, 218, 156)-Net over F₃ — Constructive and digital

Digital (132, 218, 156)-net over F₃, using

2 times m-reduction [i] based on digital (132, 220, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 110, 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]

(218−86, 218, 209)-Net over F₃ — Digital

Digital (132, 218, 209)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−86, 218, 2172)-Net in Base 3 — Upper bound on s

There is no (132, 218, 2173)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 103 654823 329480 556095 064051 943551 628066 070794 730729 075788 488478 649228 065044 161733 794428 335894 017963 609515 > 3²¹⁸ [i]