MinT - Best Known (131−57, 131, s)-Nets in Base 5

Best Known (131−57, 131, s)-Nets in Base 5

(131−57, 131, 132)-Net over F₅ — Constructive and digital

Digital (74, 131, 132)-net over F₅, using

9 times m-reduction [i] based on digital (74, 140, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 70, 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]

(131−57, 131, 210)-Net over F₅ — Digital

Digital (74, 131, 210)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−57, 131, 4947)-Net in Base 5 — Upper bound on s

There is no (74, 131, 4948)-net in base 5, because

1 times m-reduction [i] would yield (74, 130, 4948)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 375187 455107 355713 268110 938841 993452 609014 954448 160742 182092 426473 182836 832585 251621 217025 > 5¹³⁰ [i]