MinT - Best Known (134−29, 134, s)-Nets in Base 5

Best Known (134−29, 134, s)-Nets in Base 5

(134−29, 134, 504)-Net over F₅ — Constructive and digital

Digital (105, 134, 504)-net over F₅, using

4 times m-reduction [i] based on digital (105, 138, 504)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (36, 52, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 26, 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 (53, 86, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 43, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(134−29, 134, 6266)-Net over F₅ — Digital

Digital (105, 134, 6266)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−29, 134, 6601036)-Net in Base 5 — Upper bound on s

There is no (105, 134, 6601037)-net in base 5, because

1 times m-reduction [i] would yield (105, 133, 6601037)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 918 356017 777724 405429 913426 683681 288559 829965 843680 736706 596291 530106 561886 645201 147448 766825 > 5¹³³ [i]