MinT - Best Known (143−39, 143, s)-Nets in Base 5

Best Known (143−39, 143, s)-Nets in Base 5

(143−39, 143, 408)-Net over F₅ — Constructive and digital

Digital (104, 143, 408)-net over F₅, using

5 times m-reduction [i] based on digital (104, 148, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 74, 204)-net over F₂₅, using
  - net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
      - a function field by GarcÃa and Quoos [i]

(143−39, 143, 1622)-Net over F₅ — Digital

Digital (104, 143, 1622)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−39, 143, 331908)-Net in Base 5 — Upper bound on s

There is no (104, 143, 331909)-net in base 5, because

1 times m-reduction [i] would yield (104, 142, 331909)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1793 694963 690180 337728 168824 220930 170616 610445 511328 880187 931936 339927 512557 699531 267308 820808 733325 > 5¹⁴² [i]