MinT - Best Known (154, 154+81, s)-Nets in Base 3

Best Known (154, 154+81, s)-Nets in Base 3

(154, 154+81, 162)-Net over F₃ — Constructive and digital

Digital (154, 235, 162)-net over F₃, using

9 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]

(154, 154+81, 331)-Net over F₃ — Digital

Digital (154, 235, 331)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+81, 4835)-Net in Base 3 — Upper bound on s

There is no (154, 235, 4836)-net in base 3, because

1 times m-reduction [i] would yield (154, 234, 4836)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4465 264178 699886 551646 227192 778914 591007 754586 208558 053357 309422 939423 502728 673336 907769 292629 690498 681495 226049 > 3²³⁴ [i]