MinT - Best Known (82−35, 82, s)-Nets in Base 5

Best Known (82−35, 82, s)-Nets in Base 5

(82−35, 82, 132)-Net over F₅ — Constructive and digital

Digital (47, 82, 132)-net over F₅, using

4 times m-reduction [i] based on digital (47, 86, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 43, 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]

(82−35, 82, 155)-Net over F₅ — Digital

Digital (47, 82, 155)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−35, 82, 3827)-Net in Base 5 — Upper bound on s

There is no (47, 82, 3828)-net in base 5, because

1 times m-reduction [i] would yield (47, 81, 3828)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 414 988018 141168 823913 680330 958337 358208 504945 522298 209745 > 5⁸¹ [i]