MinT - Best Known (134−43, 134, s)-Nets in Base 5

Best Known (134−43, 134, s)-Nets in Base 5

(134−43, 134, 296)-Net over F₅ — Constructive and digital

Digital (91, 134, 296)-net over F₅, using

10 times m-reduction [i] based on digital (91, 144, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 72, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(134−43, 134, 720)-Net over F₅ — Digital

Digital (91, 134, 720)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−43, 134, 57959)-Net in Base 5 — Upper bound on s

There is no (91, 134, 57960)-net in base 5, because

1 times m-reduction [i] would yield (91, 133, 57960)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 918 355666 405453 793561 466643 941044 400670 218787 570950 574080 940735 829428 512671 237890 358711 453345 > 5¹³³ [i]