MinT - Best Known (72−29, 72, s)-Nets in Base 5

Best Known (72−29, 72, s)-Nets in Base 5

(72−29, 72, 132)-Net over F₅ — Constructive and digital

Digital (43, 72, 132)-net over F₅, using

6 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]

(72−29, 72, 174)-Net over F₅ — Digital

Digital (43, 72, 174)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−29, 72, 5288)-Net in Base 5 — Upper bound on s

There is no (43, 72, 5289)-net in base 5, because

1 times m-reduction [i] would yield (43, 71, 5289)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 42 377808 066521 643220 506728 837589 728781 604057 622505 > 5⁷¹ [i]