MinT - Best Known (71, 71+35, s)-Nets in Base 3

Best Known (71, 71+35, s)-Nets in Base 3

(71, 71+35, 148)-Net over F₃ — Constructive and digital

Digital (71, 106, 148)-net over F₃, using

2 times m-reduction [i] based on digital (71, 108, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 54, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(71, 71+35, 194)-Net over F₃ — Digital

Digital (71, 106, 194)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+35, 3159)-Net in Base 3 — Upper bound on s

There is no (71, 106, 3160)-net in base 3, because

1 times m-reduction [i] would yield (71, 105, 3160)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 125 744455 232052 854169 381280 601926 322068 432125 245361 > 3¹⁰⁵ [i]