MinT - Best Known (146−46, 146, s)-Nets in Base 3

Best Known (146−46, 146, s)-Nets in Base 3

(146−46, 146, 156)-Net over F₃ — Constructive and digital

Digital (100, 146, 156)-net over F₃, using

10 times m-reduction [i] based on digital (100, 156, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 78, 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]

(146−46, 146, 290)-Net over F₃ — Digital

Digital (100, 146, 290)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−46, 146, 5013)-Net in Base 3 — Upper bound on s

There is no (100, 146, 5014)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4571 677381 867303 739644 280449 754449 842646 727345 905639 274910 694218 644025 > 3¹⁴⁶ [i]