MinT - Best Known (70−29, 70, s)-Nets in Base 5

Best Known (70−29, 70, s)-Nets in Base 5

(70−29, 70, 132)-Net over F₅ — Constructive and digital

Digital (41, 70, 132)-net over F₅, using

4 times m-reduction [i] based on digital (41, 74, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 37, 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]

(70−29, 70, 153)-Net over F₅ — Digital

Digital (41, 70, 153)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−29, 70, 4200)-Net in Base 5 — Upper bound on s

There is no (41, 70, 4201)-net in base 5, because

1 times m-reduction [i] would yield (41, 69, 4201)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 697510 165380 735464 344486 344917 988059 235781 838825 > 5⁶⁹ [i]