MinT - Best Known (129−55, 129, s)-Nets in Base 3

Best Known (129−55, 129, s)-Nets in Base 3

(129−55, 129, 80)-Net over F₃ — Constructive and digital

Digital (74, 129, 80)-net over F₃, using

3 times m-reduction [i] based on digital (74, 132, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 66, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(129−55, 129, 108)-Net over F₃ — Digital

Digital (74, 129, 108)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−55, 129, 972)-Net in Base 3 — Upper bound on s

There is no (74, 129, 973)-net in base 3, because

1 times m-reduction [i] would yield (74, 128, 973)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 12 066059 089404 803188 781811 133590 127038 305657 784172 188368 476203 > 3¹²⁸ [i]