MinT - Best Known (141−40, 141, s)-Nets in Base 5

Best Known (141−40, 141, s)-Nets in Base 5

(141−40, 141, 408)-Net over F₅ — Constructive and digital

Digital (101, 141, 408)-net over F₅, using

1 times m-reduction [i] based on digital (101, 142, 408)-net over F₅, using
- trace code for nets [i] based on digital (30, 71, 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]

(141−40, 141, 1315)-Net over F₅ — Digital

Digital (101, 141, 1315)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−40, 141, 175771)-Net in Base 5 — Upper bound on s

There is no (101, 141, 175772)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 358 744764 967528 862253 166752 733937 941103 998845 668932 582746 207534 770717 717597 746477 776320 467447 217921 > 5¹⁴¹ [i]