MinT - Best Known (141−63, 141, s)-Nets in Base 5

Best Known (141−63, 141, s)-Nets in Base 5

(141−63, 141, 132)-Net over F₅ — Constructive and digital

Digital (78, 141, 132)-net over F₅, using

7 times m-reduction [i] based on digital (78, 148, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 74, 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]

(141−63, 141, 203)-Net over F₅ — Digital

Digital (78, 141, 203)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−63, 141, 4429)-Net in Base 5 — Upper bound on s

There is no (78, 141, 4430)-net in base 5, because

1 times m-reduction [i] would yield (78, 140, 4430)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 810860 268821 668250 029850 901699 562886 077611 896788 064894 401979 302185 147297 537711 082287 631484 669785 > 5¹⁴⁰ [i]