MinT - Best Known (66, 66+47, s)-Nets in Base 5

Best Known (66, 66+47, s)-Nets in Base 5

(66, 66+47, 208)-Net over F₅ — Constructive and digital

Digital (66, 113, 208)-net over F₅, using

1 times m-reduction [i] based on digital (66, 114, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 57, 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]

(66, 66+47, 219)-Net over F₅ — Digital

Digital (66, 113, 219)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+47, 5954)-Net in Base 5 — Upper bound on s

There is no (66, 113, 5955)-net in base 5, because

1 times m-reduction [i] would yield (66, 112, 5955)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 928387 566686 000713 412997 410591 351830 691951 997977 722790 514955 820804 346209 646965 > 5¹¹² [i]