MinT - Best Known (70, 70+57, s)-Nets in Base 5

Best Known (70, 70+57, s)-Nets in Base 5

(70, 70+57, 132)-Net over F₅ — Constructive and digital

Digital (70, 127, 132)-net over F₅, using

5 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+57, 183)-Net over F₅ — Digital

Digital (70, 127, 183)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+57, 3926)-Net in Base 5 — Upper bound on s

There is no (70, 127, 3927)-net in base 5, because

1 times m-reduction [i] would yield (70, 126, 3927)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 11760 924940 564244 756811 843807 023853 299046 505094 168665 823584 655300 754958 240786 395687 342225 > 5¹²⁶ [i]