MinT - Best Known (136−45, 136, s)-Nets in Base 5

Best Known (136−45, 136, s)-Nets in Base 5

(136−45, 136, 296)-Net over F₅ — Constructive and digital

Digital (91, 136, 296)-net over F₅, using

8 times m-reduction [i] based on digital (91, 144, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 72, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(136−45, 136, 633)-Net over F₅ — Digital

Digital (91, 136, 633)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−45, 136, 44032)-Net in Base 5 — Upper bound on s

There is no (91, 136, 44033)-net in base 5, because

1 times m-reduction [i] would yield (91, 135, 44033)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 22969 203713 976481 031839 736447 458266 160761 676160 525191 829958 956636 927557 695244 609321 980443 749065 > 5¹³⁵ [i]