MinT - Best Known (46−16, 46, s)-Nets in Base 5

Best Known (46−16, 46, s)-Nets in Base 5

(46−16, 46, 132)-Net over F₅ — Constructive and digital

Digital (30, 46, 132)-net over F₅, using

6 times m-reduction [i] based on digital (30, 52, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 26, 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]

(46−16, 46, 231)-Net over F₅ — Digital

Digital (30, 46, 231)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(46−16, 46, 9827)-Net in Base 5 — Upper bound on s

There is no (30, 46, 9828)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 142 109782 754053 555690 406864 538625 > 5⁴⁶ [i]