MinT - Best Known (21, 31, s)-Nets in Base 5

Best Known (21, 31, s)-Nets in Base 5

(21, 31, 132)-Net over F₅ — Constructive and digital

Digital (21, 31, 132)-net over F₅, using

3 times m-reduction [i] based on digital (21, 34, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 17, 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]

(21, 31, 269)-Net over F₅ — Digital

Digital (21, 31, 269)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(21, 31, 14037)-Net in Base 5 — Upper bound on s

There is no (21, 31, 14038)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4657 442743 953119 963353 > 5³¹ [i]