MinT - Best Known (55−21, 55, s)-Nets in Base 5

Best Known (55−21, 55, s)-Nets in Base 5

(55−21, 55, 132)-Net over F₅ — Constructive and digital

Digital (34, 55, 132)-net over F₅, using

5 times m-reduction [i] based on digital (34, 60, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 30, 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]

(55−21, 55, 181)-Net over F₅ — Digital

Digital (34, 55, 181)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−21, 55, 6728)-Net in Base 5 — Upper bound on s

There is no (34, 55, 6729)-net in base 5, because

1 times m-reduction [i] would yield (34, 54, 6729)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 55 571986 981125 766649 869141 525657 807865 > 5⁵⁴ [i]