MinT - Best Known (119−26, 119, s)-Nets in Base 5

Best Known (119−26, 119, s)-Nets in Base 5

(119−26, 119, 504)-Net over F₅ — Constructive and digital

Digital (93, 119, 504)-net over F₅, using

1 times m-reduction [i] based on digital (93, 120, 504)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (33, 46, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 23, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
        the Hermitian function field over F₂₅ [i]
  2. digital (47, 74, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 37, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(119−26, 119, 5416)-Net over F₅ — Digital

Digital (93, 119, 5416)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−26, 119, 3544940)-Net in Base 5 — Upper bound on s

There is no (93, 119, 3544941)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 150463 600963 913345 723142 327080 062054 726465 853991 068137 954952 105479 773517 716395 570245 > 5¹¹⁹ [i]