MinT - Best Known (64−24, 64, s)-Nets in Base 5

Best Known (64−24, 64, s)-Nets in Base 5

(64−24, 64, 132)-Net over F₅ — Constructive and digital

Digital (40, 64, 132)-net over F₅, using

8 times m-reduction [i] based on digital (40, 72, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 36, 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]

(64−24, 64, 214)-Net over F₅ — Digital

Digital (40, 64, 214)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(64−24, 64, 7056)-Net in Base 5 — Upper bound on s

There is no (40, 64, 7057)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 542 119422 422045 732376 609147 250745 035238 636625 > 5⁶⁴ [i]