MinT - Best Known (69, 69+57, s)-Nets in Base 5

Best Known (69, 69+57, s)-Nets in Base 5

(69, 69+57, 132)-Net over F₅ — Constructive and digital

Digital (69, 126, 132)-net over F₅, using

4 times m-reduction [i] based on digital (69, 130, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 65, 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]

(69, 69+57, 177)-Net over F₅ — Digital

Digital (69, 126, 177)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+57, 3706)-Net in Base 5 — Upper bound on s

There is no (69, 126, 3707)-net in base 5, because

1 times m-reduction [i] would yield (69, 125, 3707)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2361 030594 135995 548497 767207 992755 140399 611496 737577 339384 643407 361678 328734 177033 626385 > 5¹²⁵ [i]