MinT - Best Known (134−59, 134, s)-Nets in Base 5

Best Known (134−59, 134, s)-Nets in Base 5

(134−59, 134, 132)-Net over F₅ — Constructive and digital

Digital (75, 134, 132)-net over F₅, using

8 times m-reduction [i] based on digital (75, 142, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 71, 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]

(134−59, 134, 205)-Net over F₅ — Digital

Digital (75, 134, 205)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−59, 134, 4663)-Net in Base 5 — Upper bound on s

There is no (75, 134, 4664)-net in base 5, because

1 times m-reduction [i] would yield (75, 133, 4664)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 921 209848 834124 960169 343891 502978 437034 103745 035104 141173 713716 978445 322641 489274 817818 548705 > 5¹³³ [i]