MinT - Best Known (58, 58+52, s)-Nets in Base 5

Best Known (58, 58+52, s)-Nets in Base 5

(58, 58+52, 104)-Net over F₅ — Constructive and digital

Digital (58, 110, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 55, 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]

(58, 58+52, 136)-Net over F₅ — Digital

Digital (58, 110, 136)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+52, 2371)-Net in Base 5 — Upper bound on s

There is no (58, 110, 2372)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77759 698199 197811 057373 730329 060565 092853 923415 497306 867209 341585 753671 215809 > 5¹¹⁰ [i]