MinT - Best Known (237−85, 237, s)-Nets in Base 3

Best Known (237−85, 237, s)-Nets in Base 3

(237−85, 237, 162)-Net over F₃ — Constructive and digital

Digital (152, 237, 162)-net over F₃, using

3 times m-reduction [i] based on digital (152, 240, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 120, 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]

(237−85, 237, 297)-Net over F₃ — Digital

Digital (152, 237, 297)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−85, 237, 3919)-Net in Base 3 — Upper bound on s

There is no (152, 237, 3920)-net in base 3, because

1 times m-reduction [i] would yield (152, 236, 3920)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40258 385060 185144 722756 475091 882060 099807 665742 072704 686061 872886 267429 470978 005707 281417 721895 117767 557610 974945 > 3²³⁶ [i]