MinT - Best Known (113, 145, s)-Nets in Base 5

Best Known (113, 145, s)-Nets in Base 5

(113, 145, 504)-Net over F₅ — Constructive and digital

Digital (113, 145, 504)-net over F₅, using

5 times m-reduction [i] based on digital (113, 150, 504)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (38, 56, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 28, 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 (57, 94, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 47, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(113, 145, 5788)-Net over F₅ — Digital

Digital (113, 145, 5788)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 145, 3671918)-Net in Base 5 — Upper bound on s

There is no (113, 145, 3671919)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 224208 208377 324632 697338 497180 423787 192971 364136 480916 463346 114301 312369 210352 323829 186898 145286 465473 > 5¹⁴⁵ [i]