MinT - Best Known (92−42, 92, s)-Nets in Base 5

Best Known (92−42, 92, s)-Nets in Base 5

(92−42, 92, 132)-Net over F₅ — Constructive and digital

Digital (50, 92, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 46, 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]

(92−42, 92, 133)-Net over F₅ — Digital

Digital (50, 92, 133)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−42, 92, 2488)-Net in Base 5 — Upper bound on s

There is no (50, 92, 2489)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 20278 017630 622808 572069 483201 126174 077107 630630 052319 289790 120405 > 5⁹² [i]