MinT - Best Known (58−20, 58, s)-Nets in Base 5

Best Known (58−20, 58, s)-Nets in Base 5

(58−20, 58, 208)-Net over F₅ — Constructive and digital

Digital (38, 58, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 29, 104)-net over F₂₅, using
- net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by GarcÃa and Quoos [i]

(58−20, 58, 279)-Net over F₅ — Digital

Digital (38, 58, 279)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58−20, 58, 12814)-Net in Base 5 — Upper bound on s

There is no (38, 58, 12815)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 34705 165960 810456 449800 250697 377982 049241 > 5⁵⁸ [i]