MinT - Best Known (58, 58+40, s)-Nets in Base 5

Best Known (58, 58+40, s)-Nets in Base 5

(58, 58+40, 208)-Net over F₅ — Constructive and digital

Digital (58, 98, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 49, 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, 58+40, 209)-Net over F₅ — Digital

Digital (58, 98, 209)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+40, 5508)-Net in Base 5 — Upper bound on s

There is no (58, 98, 5509)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 315 748115 250353 351369 641727 286802 625191 576510 858691 767221 222648 629425 > 5⁹⁸ [i]