MinT - Best Known (93−42, 93, s)-Nets in Base 5

Best Known (93−42, 93, s)-Nets in Base 5

(93−42, 93, 132)-Net over F₅ — Constructive and digital

Digital (51, 93, 132)-net over F₅, using

1 times m-reduction [i] based on digital (51, 94, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 47, 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]

(93−42, 93, 140)-Net over F₅ — Digital

Digital (51, 93, 140)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−42, 93, 2687)-Net in Base 5 — Upper bound on s

There is no (51, 93, 2688)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 101023 369975 703233 879044 051496 826588 128099 621011 227279 485022 288385 > 5⁹³ [i]