MinT - Best Known (68−25, 68, s)-Nets in Base 5

Best Known (68−25, 68, s)-Nets in Base 5

(68−25, 68, 208)-Net over F₅ — Constructive and digital

Digital (43, 68, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 34, 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]

(68−25, 68, 243)-Net over F₅ — Digital

Digital (43, 68, 243)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(68−25, 68, 10556)-Net in Base 5 — Upper bound on s

There is no (43, 68, 10557)-net in base 5, because

1 times m-reduction [i] would yield (43, 67, 10557)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 67773 879087 436145 967001 839209 890864 589108 796625 > 5⁶⁷ [i]