MinT - Best Known (141−65, 141, s)-Nets in Base 5

Best Known (141−65, 141, s)-Nets in Base 5

(141−65, 141, 132)-Net over F₅ — Constructive and digital

Digital (76, 141, 132)-net over F₅, using

3 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]

(141−65, 141, 182)-Net over F₅ — Digital

Digital (76, 141, 182)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−65, 141, 3630)-Net in Base 5 — Upper bound on s

There is no (76, 141, 3631)-net in base 5, because

1 times m-reduction [i] would yield (76, 140, 3631)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 785693 788906 988593 926066 097184 076236 328457 428419 842414 394730 429594 988592 302910 061742 231366 602625 > 5¹⁴⁰ [i]