MinT - Best Known (133−30, 133, s)-Nets in Base 5

Best Known (133−30, 133, s)-Nets in Base 5

(133−30, 133, 504)-Net over F₅ — Constructive and digital

Digital (103, 133, 504)-net over F₅, using

5¹ times duplication [i] based on digital (102, 132, 504)-net over F₅, using
- t-expansion [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)

(133−30, 133, 4699)-Net over F₅ — Digital

Digital (103, 133, 4699)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−30, 133, 2530689)-Net in Base 5 — Upper bound on s

There is no (103, 133, 2530690)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 918 358321 557563 158703 858557 294914 351236 149966 650229 018914 098119 295666 908165 873360 723051 160105 > 5¹³³ [i]