MinT - Best Known (70−27, 70, s)-Nets in Base 5

Best Known (70−27, 70, s)-Nets in Base 5

(70−27, 70, 132)-Net over F₅ — Constructive and digital

Digital (43, 70, 132)-net over F₅, using

8 times m-reduction [i] based on digital (43, 78, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 39, 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]

(70−27, 70, 202)-Net over F₅ — Digital

Digital (43, 70, 202)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−27, 70, 7256)-Net in Base 5 — Upper bound on s

There is no (43, 70, 7257)-net in base 5, because

1 times m-reduction [i] would yield (43, 69, 7257)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 696409 068461 169202 587438 043063 822558 119942 395125 > 5⁶⁹ [i]