MinT - Best Known (136−63, 136, s)-Nets in Base 5

Best Known (136−63, 136, s)-Nets in Base 5

(136−63, 136, 132)-Net over F₅ — Constructive and digital

Digital (73, 136, 132)-net over F₅, using

2 times m-reduction [i] based on digital (73, 138, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 69, 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]

(136−63, 136, 174)-Net over F₅ — Digital

Digital (73, 136, 174)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−63, 136, 3411)-Net in Base 5 — Upper bound on s

There is no (73, 136, 3412)-net in base 5, because

1 times m-reduction [i] would yield (73, 135, 3412)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 22981 389102 735420 847229 853519 230812 838343 935189 851715 358693 289029 363231 749636 195609 676437 447633 > 5¹³⁵ [i]