MinT - Best Known (240−97, 240, s)-Nets in Base 3

Best Known (240−97, 240, s)-Nets in Base 3

(240−97, 240, 156)-Net over F₃ — Constructive and digital

Digital (143, 240, 156)-net over F₃, using

2 times m-reduction [i] based on digital (143, 242, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 121, 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]

(240−97, 240, 213)-Net over F₃ — Digital

Digital (143, 240, 213)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−97, 240, 2178)-Net in Base 3 — Upper bound on s

There is no (143, 240, 2179)-net in base 3, because

1 times m-reduction [i] would yield (143, 239, 2179)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 090200 576604 110722 064248 196857 187239 562965 321321 468199 302982 716215 184480 778539 816179 332069 725765 609080 873165 986465 > 3²³⁹ [i]