MinT - Best Known (75−30, 75, s)-Nets in Base 5

Best Known (75−30, 75, s)-Nets in Base 5

(75−30, 75, 132)-Net over F₅ — Constructive and digital

Digital (45, 75, 132)-net over F₅, using

7 times m-reduction [i] based on digital (45, 82, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 41, 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]

(75−30, 75, 184)-Net over F₅ — Digital

Digital (45, 75, 184)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−30, 75, 5007)-Net in Base 5 — Upper bound on s

There is no (45, 75, 5008)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 26504 694864 023175 095897 680843 900020 630430 678556 546625 > 5⁷⁵ [i]