MinT - Best Known (136, 136+107, s)-Nets in Base 3

Best Known (136, 136+107, s)-Nets in Base 3

(136, 136+107, 128)-Net over F₃ — Constructive and digital

Digital (136, 243, 128)-net over F₃, using

3 times m-reduction [i] based on digital (136, 246, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 123, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(136, 136+107, 169)-Net over F₃ — Digital

Digital (136, 243, 169)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+107, 1501)-Net in Base 3 — Upper bound on s

There is no (136, 243, 1502)-net in base 3, because

1 times m-reduction [i] would yield (136, 242, 1502)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 323516 317683 832113 403840 735384 796510 384333 659123 137003 821227 165095 336012 286437 528561 435561 977801 568695 495624 234869 > 3²⁴² [i]