MinT - Best Known (231−83, 231, s)-Nets in Base 3

Best Known (231−83, 231, s)-Nets in Base 3

(231−83, 231, 162)-Net over F₃ — Constructive and digital

Digital (148, 231, 162)-net over F₃, using

1 times m-reduction [i] based on digital (148, 232, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 116, 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]

(231−83, 231, 288)-Net over F₃ — Digital

Digital (148, 231, 288)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−83, 231, 3791)-Net in Base 3 — Upper bound on s

There is no (148, 231, 3792)-net in base 3, because

1 times m-reduction [i] would yield (148, 230, 3792)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 921720 922631 515198 652993 932287 274099 185006 488118 780337 805180 798470 643767 565620 153613 773771 959096 326644 632225 > 3²³⁰ [i]