MinT - Best Known (40, 40+23, s)-Nets in Base 5

Best Known (40, 40+23, s)-Nets in Base 5

(40, 40+23, 132)-Net over F₅ — Constructive and digital

Digital (40, 63, 132)-net over F₅, using

9 times m-reduction [i] based on digital (40, 72, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 36, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(40, 40+23, 238)-Net over F₅ — Digital

Digital (40, 63, 238)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+23, 10673)-Net in Base 5 — Upper bound on s

There is no (40, 63, 10674)-net in base 5, because

1 times m-reduction [i] would yield (40, 62, 10674)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 21 705498 310658 553613 335091 837236 703896 092777 > 5⁶² [i]