MinT - Best Known (121−55, 121, s)-Nets in Base 5

Best Known (121−55, 121, s)-Nets in Base 5

(121−55, 121, 132)-Net over F₅ — Constructive and digital

Digital (66, 121, 132)-net over F₅, using

3 times m-reduction [i] based on digital (66, 124, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 62, 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]

(121−55, 121, 168)-Net over F₅ — Digital

Digital (66, 121, 168)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−55, 121, 3470)-Net in Base 5 — Upper bound on s

There is no (66, 121, 3471)-net in base 5, because

1 times m-reduction [i] would yield (66, 120, 3471)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 753891 361971 066224 282754 868499 676329 137012 774820 122077 045872 985693 796271 272316 565205 > 5¹²⁰ [i]