MinT - Best Known (56, 56+38, s)-Nets in Base 5

Best Known (56, 56+38, s)-Nets in Base 5

(56, 56+38, 208)-Net over F₅ — Constructive and digital

Digital (56, 94, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 47, 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]

(56, 56+38, 209)-Net over F₅ — Digital

Digital (56, 94, 209)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+38, 5677)-Net in Base 5 — Upper bound on s

There is no (56, 94, 5678)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 505473 405144 501870 429520 040053 974718 289224 368428 070747 817130 859225 > 5⁹⁴ [i]