MinT - Best Known (55, 55+41, s)-Nets in Base 5

Best Known (55, 55+41, s)-Nets in Base 5

(55, 55+41, 132)-Net over F₅ — Constructive and digital

Digital (55, 96, 132)-net over F₅, using

6 times m-reduction [i] based on digital (55, 102, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 51, 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, 55+41, 175)-Net over F₅ — Digital

Digital (55, 96, 175)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+41, 4324)-Net in Base 5 — Upper bound on s

There is no (55, 96, 4325)-net in base 5, because

1 times m-reduction [i] would yield (55, 95, 4325)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 534160 196651 381384 891516 255754 682808 987020 239366 802083 100782 542001 > 5⁹⁵ [i]