MinT - Best Known (70, 70+64, s)-Nets in Base 5

Best Known (70, 70+64, s)-Nets in Base 5

(70, 70+64, 104)-Net over F₅ — Constructive and digital

Digital (70, 134, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 67, 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]

(70, 70+64, 155)-Net over F₅ — Digital

Digital (70, 134, 155)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+64, 2679)-Net in Base 5 — Upper bound on s

There is no (70, 134, 2680)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4645 342892 673969 648590 465303 337629 019962 523866 465188 378491 445303 741660 450737 648302 665654 595585 > 5¹³⁴ [i]