MinT - Best Known (182−67, 182, s)-Nets in Base 3

Best Known (182−67, 182, s)-Nets in Base 3

(182−67, 182, 156)-Net over F₃ — Constructive and digital

Digital (115, 182, 156)-net over F₃, using

4 times m-reduction [i] based on digital (115, 186, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 93, 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]

(182−67, 182, 218)-Net over F₃ — Digital

Digital (115, 182, 218)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−67, 182, 2692)-Net in Base 3 — Upper bound on s

There is no (115, 182, 2693)-net in base 3, because

1 times m-reduction [i] would yield (115, 181, 2693)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 231 303655 198112 062131 241085 461019 728765 089251 413751 635368 290500 792188 796459 817858 637963 > 3¹⁸¹ [i]