MinT - Best Known (48−19, 48, s)-Nets in Base 5

Best Known (48−19, 48, s)-Nets in Base 5

(48−19, 48, 132)-Net over F₅ — Constructive and digital

Digital (29, 48, 132)-net over F₅, using

2 times m-reduction [i] based on digital (29, 50, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 25, 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]

(48−19, 48, 144)-Net over F₅ — Digital

Digital (29, 48, 144)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(48−19, 48, 4626)-Net in Base 5 — Upper bound on s

There is no (29, 48, 4627)-net in base 5, because

1 times m-reduction [i] would yield (29, 47, 4627)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 710 797423 718242 912611 592661 230125 > 5⁴⁷ [i]