MinT - Best Known (130−56, 130, s)-Nets in Base 5

Best Known (130−56, 130, s)-Nets in Base 5

(130−56, 130, 208)-Net over F₅ — Constructive and digital

Digital (74, 130, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 65, 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]

(130−56, 130, 217)-Net over F₅ — Digital

Digital (74, 130, 217)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−56, 130, 4947)-Net in Base 5 — Upper bound on s

There is no (74, 130, 4948)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 375187 455107 355713 268110 938841 993452 609014 954448 160742 182092 426473 182836 832585 251621 217025 > 5¹³⁰ [i]