MinT - Best Known (133−59, 133, s)-Nets in Base 5

Best Known (133−59, 133, s)-Nets in Base 5

(133−59, 133, 132)-Net over F₅ — Constructive and digital

Digital (74, 133, 132)-net over F₅, using

7 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]

(133−59, 133, 198)-Net over F₅ — Digital

Digital (74, 133, 198)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−59, 133, 4410)-Net in Base 5 — Upper bound on s

There is no (74, 133, 4411)-net in base 5, because

1 times m-reduction [i] would yield (74, 132, 4411)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 184 162247 181006 027436 755174 737296 106693 230377 838430 242676 176295 818875 742141 503694 001111 357565 > 5¹³² [i]