MinT - Best Known (93−39, 93, s)-Nets in Base 5

Best Known (93−39, 93, s)-Nets in Base 5

(93−39, 93, 132)-Net over F₅ — Constructive and digital

Digital (54, 93, 132)-net over F₅, using

7 times m-reduction [i] based on digital (54, 100, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 50, 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]

(93−39, 93, 182)-Net over F₅ — Digital

Digital (54, 93, 182)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−39, 93, 4790)-Net in Base 5 — Upper bound on s

There is no (54, 93, 4791)-net in base 5, because

1 times m-reduction [i] would yield (54, 92, 4791)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 20219 289905 362069 012181 425055 928526 327090 131286 562361 268129 992725 > 5⁹² [i]