MinT - Best Known (136−41, 136, s)-Nets in Base 3

Best Known (136−41, 136, s)-Nets in Base 3

(136−41, 136, 192)-Net over F₃ — Constructive and digital

Digital (95, 136, 192)-net over F₃, using

3¹ times duplication [i] based on digital (94, 135, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 45, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(136−41, 136, 316)-Net over F₃ — Digital

Digital (95, 136, 316)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−41, 136, 6880)-Net in Base 3 — Upper bound on s

There is no (95, 136, 6881)-net in base 3, because

1 times m-reduction [i] would yield (95, 135, 6881)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25826 022156 640019 762440 678280 833661 844008 083477 927023 551416 228497 > 3¹³⁵ [i]