MinT - Best Known (69, 69+51, s)-Nets in Base 5

Best Known (69, 69+51, s)-Nets in Base 5

(69, 69+51, 208)-Net over F₅ — Constructive and digital

Digital (69, 120, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 60, 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]

(69, 69+51, 213)-Net over F₅ — Digital

Digital (69, 120, 213)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+51, 5385)-Net in Base 5 — Upper bound on s

There is no (69, 120, 5386)-net in base 5, because

1 times m-reduction [i] would yield (69, 119, 5386)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 151075 987416 405088 522085 718039 220197 118764 434830 182941 478895 928847 410408 844080 242985 > 5¹¹⁹ [i]