MinT - Best Known (30−10, 30, s)-Nets in Base 5

Best Known (30−10, 30, s)-Nets in Base 5

(30−10, 30, 132)-Net over F₅ — Constructive and digital

Digital (20, 30, 132)-net over F₅, using

2 times m-reduction [i] based on digital (20, 32, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 16, 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]

(30−10, 30, 226)-Net over F₅ — Digital

Digital (20, 30, 226)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(30−10, 30, 10173)-Net in Base 5 — Upper bound on s

There is no (20, 30, 10174)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 931 688722 578866 374521 > 5³⁰ [i]