MinT - Best Known (237−83, 237, s)-Nets in Base 3

Best Known (237−83, 237, s)-Nets in Base 3

(237−83, 237, 162)-Net over F₃ — Constructive and digital

Digital (154, 237, 162)-net over F₃, using

7 times m-reduction [i] based on digital (154, 244, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 122, 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]

(237−83, 237, 318)-Net over F₃ — Digital

Digital (154, 237, 318)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−83, 237, 4459)-Net in Base 3 — Upper bound on s

There is no (154, 237, 4460)-net in base 3, because

1 times m-reduction [i] would yield (154, 236, 4460)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 39892 676539 869593 057382 641986 255998 987372 906413 723621 482230 989125 253987 481988 688380 725836 836184 078023 441853 839449 > 3²³⁶ [i]