MinT - Best Known (145−69, 145, s)-Nets in Base 5

Best Known (145−69, 145, s)-Nets in Base 5

(145−69, 145, 104)-Net over F₅ — Constructive and digital

Digital (76, 145, 104)-net over F₅, using

1 times m-reduction [i] based on digital (76, 146, 104)-net over F₅, using
- trace code for nets [i] based on digital (3, 73, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]

(145−69, 145, 168)-Net over F₅ — Digital

Digital (76, 145, 168)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−69, 145, 3063)-Net in Base 5 — Upper bound on s

There is no (76, 145, 3064)-net in base 5, because

1 times m-reduction [i] would yield (76, 144, 3064)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 45013 170056 911884 058109 892067 693946 724119 468571 785050 173502 718349 180959 001137 565638 939601 547552 113025 > 5¹⁴⁴ [i]