MinT - Best Known (239−82, 239, s)-Nets in Base 3

Best Known (239−82, 239, s)-Nets in Base 3

(239−82, 239, 162)-Net over F₃ — Constructive and digital

Digital (157, 239, 162)-net over F₃, using

11 times m-reduction [i] based on digital (157, 250, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 125, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(239−82, 239, 340)-Net over F₃ — Digital

Digital (157, 239, 340)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−82, 239, 4836)-Net in Base 3 — Upper bound on s

There is no (157, 239, 4837)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 079888 730481 167386 406005 056338 753546 534703 728404 804111 709030 758377 485951 766686 066568 284251 340179 829555 424426 151595 > 3²³⁹ [i]