MinT - Best Known (237−82, 237, s)-Nets in Base 3

Best Known (237−82, 237, s)-Nets in Base 3

(237−82, 237, 162)-Net over F₃ — Constructive and digital

Digital (155, 237, 162)-net over F₃, using

9 times m-reduction [i] based on digital (155, 246, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 123, 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]

(237−82, 237, 329)-Net over F₃ — Digital

Digital (155, 237, 329)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−82, 237, 4582)-Net in Base 3 — Upper bound on s

There is no (155, 237, 4583)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 120514 273294 413338 672814 705904 806506 352642 988910 985798 163405 328360 757284 827852 704642 502274 863790 578839 957666 941823 > 3²³⁷ [i]