MinT - Best Known (44, 70, s)-Nets in Base 5

Best Known (44, 70, s)-Nets in Base 5

(44, 70, 208)-Net over F₅ — Constructive and digital

Digital (44, 70, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 35, 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]

(44, 70, 237)-Net over F₅ — Digital

Digital (44, 70, 237)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 70, 8213)-Net in Base 5 — Upper bound on s

There is no (44, 70, 8214)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8 473490 968852 515237 858724 304001 077088 047790 809049 > 5⁷⁰ [i]