MinT - Best Known (39, 39+20, s)-Nets in Base 5

Best Known (39, 39+20, s)-Nets in Base 5

(39, 39+20, 208)-Net over F₅ — Constructive and digital

Digital (39, 59, 208)-net over F₅, using

1 times m-reduction [i] based on digital (39, 60, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 30, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

(39, 39+20, 303)-Net over F₅ — Digital

Digital (39, 59, 303)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+20, 15053)-Net in Base 5 — Upper bound on s

There is no (39, 59, 15054)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 173530 020257 441915 181074 304163 910565 647745 > 5⁵⁹ [i]