MinT - Best Known (71, 71+57, s)-Nets in Base 5

Best Known (71, 71+57, s)-Nets in Base 5

(71, 71+57, 132)-Net over F₅ — Constructive and digital

Digital (71, 128, 132)-net over F₅, using

6 times m-reduction [i] based on digital (71, 134, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 67, 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]

(71, 71+57, 190)-Net over F₅ — Digital

Digital (71, 128, 190)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+57, 4160)-Net in Base 5 — Upper bound on s

There is no (71, 128, 4161)-net in base 5, because

1 times m-reduction [i] would yield (71, 127, 4161)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 58983 858241 953235 537948 693928 029469 146099 904270 649002 201570 779621 006948 643664 358853 283345 > 5¹²⁷ [i]