MinT - Best Known (147−54, 147, s)-Nets in Base 5

Best Known (147−54, 147, s)-Nets in Base 5

(147−54, 147, 296)-Net over F₅ — Constructive and digital

Digital (93, 147, 296)-net over F₅, using

1 times m-reduction [i] based on digital (93, 148, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 74, 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]

(147−54, 147, 434)-Net over F₅ — Digital

Digital (93, 147, 434)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−54, 147, 17432)-Net in Base 5 — Upper bound on s

There is no (93, 147, 17433)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 609911 579983 852198 007213 440237 908639 899144 097685 221006 142419 639474 404967 291496 924359 911855 792815 218813 > 5¹⁴⁷ [i]