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

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

(58, 58+20, 296)-Net over F₅ — Constructive and digital

Digital (58, 78, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 39, 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]

(58, 58+20, 1477)-Net over F₅ — Digital

Digital (58, 78, 1477)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+20, 320533)-Net in Base 5 — Upper bound on s

There is no (58, 78, 320534)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 308817 045540 041584 828721 258414 682597 009911 025709 854465 > 5⁷⁸ [i]