MinT - Best Known (71, 71+55, s)-Nets in Base 5

Best Known (71, 71+55, s)-Nets in Base 5

(71, 71+55, 132)-Net over F₅ — Constructive and digital

Digital (71, 126, 132)-net over F₅, using

8 times m-reduction [i] based on digital (71, 134, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 67, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(71, 71+55, 201)-Net over F₅ — Digital

Digital (71, 126, 201)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+55, 4682)-Net in Base 5 — Upper bound on s

There is no (71, 126, 4683)-net in base 5, because

1 times m-reduction [i] would yield (71, 125, 4683)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2355 396226 766410 327207 877413 537464 433146 965049 141787 342555 440686 935182 152187 524197 568773 > 5¹²⁵ [i]