MinT - Best Known (140−63, 140, s)-Nets in Base 5

Best Known (140−63, 140, s)-Nets in Base 5

(140−63, 140, 132)-Net over F₅ — Constructive and digital

Digital (77, 140, 132)-net over F₅, using

6 times m-reduction [i] based on digital (77, 146, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 73, 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]

(140−63, 140, 197)-Net over F₅ — Digital

Digital (77, 140, 197)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−63, 140, 4204)-Net in Base 5 — Upper bound on s

There is no (77, 140, 4205)-net in base 5, because

1 times m-reduction [i] would yield (77, 139, 4205)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 390868 194050 671635 432209 939315 250584 162527 626759 565921 506002 674074 937792 303656 281973 325228 604605 > 5¹³⁹ [i]