MinT - Best Known (134−61, 134, s)-Nets in Base 5

Best Known (134−61, 134, s)-Nets in Base 5

(134−61, 134, 132)-Net over F₅ — Constructive and digital

Digital (73, 134, 132)-net over F₅, using

4 times m-reduction [i] based on digital (73, 138, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 69, 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]

(134−61, 134, 182)-Net over F₅ — Digital

Digital (73, 134, 182)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−61, 134, 3758)-Net in Base 5 — Upper bound on s

There is no (73, 134, 3759)-net in base 5, because

1 times m-reduction [i] would yield (73, 133, 3759)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 925 086647 279120 480230 751289 911893 484884 519565 704035 026440 807158 663666 980899 861592 633759 942025 > 5¹³³ [i]