MinT - Best Known (70, 70+61, s)-Nets in Base 5

Best Known (70, 70+61, s)-Nets in Base 5

(70, 70+61, 132)-Net over F₅ — Constructive and digital

Digital (70, 131, 132)-net over F₅, using

1 times m-reduction [i] based on digital (70, 132, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 66, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(70, 70+61, 165)-Net over F₅ — Digital

Digital (70, 131, 165)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+61, 3196)-Net in Base 5 — Upper bound on s

There is no (70, 131, 3197)-net in base 5, because

1 times m-reduction [i] would yield (70, 130, 3197)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 405453 782255 240889 998276 419121 835810 886970 279280 823601 260386 481202 368969 537089 395580 778793 > 5¹³⁰ [i]