MinT - Best Known (92, 92+25, s)-Nets in Base 5

Best Known (92, 92+25, s)-Nets in Base 5

(92, 92+25, 504)-Net over F₅ — Constructive and digital

Digital (92, 117, 504)-net over F₅, using

1 times m-reduction [i] based on digital (92, 118, 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 (46, 72, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 36, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(92, 92+25, 6275)-Net over F₅ — Digital

Digital (92, 117, 6275)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(92, 92+25, 7551113)-Net in Base 5 — Upper bound on s

There is no (92, 117, 7551114)-net in base 5, because

1 times m-reduction [i] would yield (92, 116, 7551114)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1203 707928 676959 657990 771448 226209 324718 858761 447527 432358 788410 137309 917576 531393 > 5¹¹⁶ [i]