MinT - Best Known (125−49, 125, s)-Nets in Base 3

Best Known (125−49, 125, s)-Nets in Base 3

(125−49, 125, 128)-Net over F₃ — Constructive and digital

Digital (76, 125, 128)-net over F₃, using

1 times m-reduction [i] based on digital (76, 126, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 63, 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]

(125−49, 125, 133)-Net over F₃ — Digital

Digital (76, 125, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−49, 125, 1407)-Net in Base 3 — Upper bound on s

There is no (76, 125, 1408)-net in base 3, because

1 times m-reduction [i] would yield (76, 124, 1408)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 147857 159054 726794 134222 319467 380415 268102 898915 901753 638913 > 3¹²⁴ [i]