MinT - Best Known (55, 104, s)-Nets in Base 5

Best Known (55, 104, s)-Nets in Base 5

(55, 104, 104)-Net over F₅ — Constructive and digital

Digital (55, 104, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 52, 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]

(55, 104, 131)-Net over F₅ — Digital

Digital (55, 104, 131)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 104, 2431)-Net in Base 5 — Upper bound on s

There is no (55, 104, 2432)-net in base 5, because

1 times m-reduction [i] would yield (55, 103, 2432)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 987192 815771 900940 593807 557733 634536 559670 338007 353345 973317 504048 513025 > 5¹⁰³ [i]