MinT - Best Known (101−41, 101, s)-Nets in Base 5

Best Known (101−41, 101, s)-Nets in Base 5

(101−41, 101, 208)-Net over F₅ — Constructive and digital

Digital (60, 101, 208)-net over F₅, using

1 times m-reduction [i] based on digital (60, 102, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 51, 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]

(101−41, 101, 218)-Net over F₅ — Digital

Digital (60, 101, 218)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−41, 101, 6473)-Net in Base 5 — Upper bound on s

There is no (60, 101, 6474)-net in base 5, because

1 times m-reduction [i] would yield (60, 100, 6474)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7905 798231 211865 507617 428746 203479 744716 919161 859821 127661 520307 673921 > 5¹⁰⁰ [i]