MinT - Best Known (75, 75+61, s)-Nets in Base 5

Best Known (75, 75+61, s)-Nets in Base 5

(75, 75+61, 132)-Net over F₅ — Constructive and digital

Digital (75, 136, 132)-net over F₅, using

6 times m-reduction [i] based on digital (75, 142, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 71, 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]

(75, 75+61, 194)-Net over F₅ — Digital

Digital (75, 136, 194)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+61, 4186)-Net in Base 5 — Upper bound on s

There is no (75, 136, 4187)-net in base 5, because

1 times m-reduction [i] would yield (75, 135, 4187)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 23087 677325 716797 395763 873261 012200 291227 355338 066635 761561 136803 191599 490334 298167 361656 435849 > 5¹³⁵ [i]