MinT - Best Known (175−55, 175, s)-Nets in Base 3

Best Known (175−55, 175, s)-Nets in Base 3

(175−55, 175, 162)-Net over F₃ — Constructive and digital

Digital (120, 175, 162)-net over F₃, using

1 times m-reduction [i] based on digital (120, 176, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 88, 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]

(175−55, 175, 341)-Net over F₃ — Digital

Digital (120, 175, 341)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−55, 175, 6462)-Net in Base 3 — Upper bound on s

There is no (120, 175, 6463)-net in base 3, because

1 times m-reduction [i] would yield (120, 174, 6463)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 104821 151713 727999 186059 568952 457805 026980 133477 390918 399505 034281 164515 821824 978123 > 3¹⁷⁴ [i]