MinT - Best Known (42, 65, s)-Nets in Base 5

Best Known (42, 65, s)-Nets in Base 5

(42, 65, 208)-Net over F₅ — Constructive and digital

Digital (42, 65, 208)-net over F₅, using

1 times m-reduction [i] based on digital (42, 66, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 33, 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]

(42, 65, 274)-Net over F₅ — Digital

Digital (42, 65, 274)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 65, 14303)-Net in Base 5 — Upper bound on s

There is no (42, 65, 14304)-net in base 5, because

1 times m-reduction [i] would yield (42, 64, 14304)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 542 155444 543237 570860 928436 667227 125821 012865 > 5⁶⁴ [i]