MinT - Best Known (130−28, 130, s)-Nets in Base 5

Best Known (130−28, 130, s)-Nets in Base 5

(130−28, 130, 504)-Net over F₅ — Constructive and digital

Digital (102, 130, 504)-net over F₅, using

t-expansion [i] based on digital (101, 130, 504)-net over F₅, using
- 2 times m-reduction [i] based on digital (101, 132, 504)-net over F₅, using
  - (u,Â u+v)-construction [i] based on
    1. digital (35, 50, 252)-net over F₅, using
      - trace code for nets [i] based on digital (10, 25, 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 (51, 82, 252)-net over F₅, using
      - trace code for nets [i] based on digital (10, 41, 126)-net over F₂₅, using
        net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(130−28, 130, 6348)-Net over F₅ — Digital

Digital (102, 130, 6348)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−28, 130, 4675548)-Net in Base 5 — Upper bound on s

There is no (102, 130, 4675549)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 346848 927423 239900 403369 422361 229117 404061 620141 004940 274937 553622 531905 651634 863998 250345 > 5¹³⁰ [i]