MinT - Best Known (134, 134+105, s)-Nets in Base 3

Best Known (134, 134+105, s)-Nets in Base 3

(134, 134+105, 128)-Net over F₃ — Constructive and digital

Digital (134, 239, 128)-net over F₃, using

3 times m-reduction [i] based on digital (134, 242, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 121, 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]

(134, 134+105, 168)-Net over F₃ — Digital

Digital (134, 239, 168)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+105, 1493)-Net in Base 3 — Upper bound on s

There is no (134, 239, 1494)-net in base 3, because

1 times m-reduction [i] would yield (134, 238, 1494)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 370017 005211 856170 558544 228247 060562 721895 328588 905478 281985 594191 778577 100570 009584 539444 017981 880718 256423 863017 > 3²³⁸ [i]