MinT - Best Known (94, 94+47, s)-Nets in Base 5

Best Known (94, 94+47, s)-Nets in Base 5

(94, 94+47, 296)-Net over F₅ — Constructive and digital

Digital (94, 141, 296)-net over F₅, using

9 times m-reduction [i] based on digital (94, 150, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 75, 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]

(94, 94+47, 630)-Net over F₅ — Digital

Digital (94, 141, 630)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+47, 42347)-Net in Base 5 — Upper bound on s

There is no (94, 141, 42348)-net in base 5, because

1 times m-reduction [i] would yield (94, 140, 42348)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 778059 302054 434599 867392 070400 832376 954828 875146 433194 830990 844760 361527 847067 900720 352890 959665 > 5¹⁴⁰ [i]