MinT - Best Known (143−67, 143, s)-Nets in Base 5

Best Known (143−67, 143, s)-Nets in Base 5

(143−67, 143, 132)-Net over F₅ — Constructive and digital

Digital (76, 143, 132)-net over F₅, using

1 times m-reduction [i] based on digital (76, 144, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 72, 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]

(143−67, 143, 175)-Net over F₅ — Digital

Digital (76, 143, 175)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−67, 143, 3325)-Net in Base 5 — Upper bound on s

There is no (76, 143, 3326)-net in base 5, because

1 times m-reduction [i] would yield (76, 142, 3326)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1805 404599 752438 045145 696355 362409 938729 025881 725252 094146 001657 805794 591606 787646 364582 727966 610425 > 5¹⁴² [i]