MinT - Best Known (114−54, 114, s)-Nets in Base 5

Best Known (114−54, 114, s)-Nets in Base 5

(114−54, 114, 104)-Net over F₅ — Constructive and digital

Digital (60, 114, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 57, 52)-net over F₂₅, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by GarcÃa and Quoos [i]

(114−54, 114, 139)-Net over F₅ — Digital

Digital (60, 114, 139)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−54, 114, 2421)-Net in Base 5 — Upper bound on s

There is no (60, 114, 2422)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 561822 852173 923722 970271 660386 309620 892872 895634 604658 183854 989931 641520 780025 > 5¹¹⁴ [i]