MinT - Best Known (139−65, 139, s)-Nets in Base 5

Best Known (139−65, 139, s)-Nets in Base 5

(139−65, 139, 132)-Net over F₅ — Constructive and digital

Digital (74, 139, 132)-net over F₅, using

1 times m-reduction [i] based on digital (74, 140, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 70, 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]

(139−65, 139, 172)-Net over F₅ — Digital

Digital (74, 139, 172)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−65, 139, 3281)-Net in Base 5 — Upper bound on s

There is no (74, 139, 3282)-net in base 5, because

1 times m-reduction [i] would yield (74, 138, 3282)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 891256 766026 140211 264279 013872 022937 131328 463820 188003 507816 841874 081200 775039 891320 425467 876865 > 5¹³⁸ [i]