MinT - Best Known (132, 201, s)-Nets in Base 3

Best Known (132, 201, s)-Nets in Base 3

(132, 201, 156)-Net over F₃ — Constructive and digital

Digital (132, 201, 156)-net over F₃, using

19 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]

(132, 201, 292)-Net over F₃ — Digital

Digital (132, 201, 292)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 201, 4302)-Net in Base 3 — Upper bound on s

There is no (132, 201, 4303)-net in base 3, because

1 times m-reduction [i] would yield (132, 200, 4303)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 267440 150837 905013 706820 371122 341995 683917 244226 150437 766735 358570 181732 669601 492765 871022 021469 > 3²⁰⁰ [i]