MinT - Best Known (129−49, 129, s)-Nets in Base 3

Best Known (129−49, 129, s)-Nets in Base 3

(129−49, 129, 128)-Net over F₃ — Constructive and digital

Digital (80, 129, 128)-net over F₃, using

5 times m-reduction [i] based on digital (80, 134, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 67, 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]

(129−49, 129, 149)-Net over F₃ — Digital

Digital (80, 129, 149)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−49, 129, 1694)-Net in Base 3 — Upper bound on s

There is no (80, 129, 1695)-net in base 3, because

1 times m-reduction [i] would yield (80, 128, 1695)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 879386 880398 853336 224589 446539 209661 233168 642113 086280 517073 > 3¹²⁸ [i]