MinT - Best Known (125−55, 125, s)-Nets in Base 5

Best Known (125−55, 125, s)-Nets in Base 5

(125−55, 125, 132)-Net over F₅ — Constructive and digital

Digital (70, 125, 132)-net over F₅, using

7 times m-reduction [i] based on digital (70, 132, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 66, 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]

(125−55, 125, 194)-Net over F₅ — Digital

Digital (70, 125, 194)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−55, 125, 4410)-Net in Base 5 — Upper bound on s

There is no (70, 125, 4411)-net in base 5, because

1 times m-reduction [i] would yield (70, 124, 4411)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 471 453831 491262 426874 962815 715478 879478 248227 153150 422435 209582 402537 007758 638974 603205 > 5¹²⁴ [i]