MinT - Best Known (143−49, 143, s)-Nets in Base 5

Best Known (143−49, 143, s)-Nets in Base 5

(143−49, 143, 296)-Net over F₅ — Constructive and digital

Digital (94, 143, 296)-net over F₅, using

7 times m-reduction [i] based on digital (94, 150, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 75, 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]

(143−49, 143, 565)-Net over F₅ — Digital

Digital (94, 143, 565)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−49, 143, 33469)-Net in Base 5 — Upper bound on s

There is no (94, 143, 33470)-net in base 5, because

1 times m-reduction [i] would yield (94, 142, 33470)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1794 397007 971336 224288 821867 653219 967961 992145 666300 872026 404123 991603 713832 245513 747696 437755 744385 > 5¹⁴² [i]