MinT - Best Known (140−32, 140, s)-Nets in Base 5

Best Known (140−32, 140, s)-Nets in Base 5

(140−32, 140, 504)-Net over F₅ — Constructive and digital

Digital (108, 140, 504)-net over F₅, using

2 times m-reduction [i] based on digital (108, 142, 504)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (37, 54, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 27, 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 (54, 88, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 44, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(140−32, 140, 4468)-Net over F₅ — Digital

Digital (108, 140, 4468)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−32, 140, 2220567)-Net in Base 5 — Upper bound on s

There is no (108, 140, 2220568)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 71 746626 591016 456865 775634 385005 797360 504360 821065 641991 722532 111995 070686 479499 351753 540610 308097 > 5¹⁴⁰ [i]