MinT - Best Known (66−28, 66, s)-Nets in Base 5

Best Known (66−28, 66, s)-Nets in Base 5

(66−28, 66, 132)-Net over F₅ — Constructive and digital

Digital (38, 66, 132)-net over F₅, using

2 times m-reduction [i] based on digital (38, 68, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 34, 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]

(66−28, 66, 134)-Net over F₅ — Digital

Digital (38, 66, 134)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(66−28, 66, 2972)-Net in Base 5 — Upper bound on s

There is no (38, 66, 2973)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 13600 414030 449212 833000 584606 235868 197534 915945 > 5⁶⁶ [i]