MinT - Best Known (49, 49+40, s)-Nets in Base 5

Best Known (49, 49+40, s)-Nets in Base 5

(49, 49+40, 132)-Net over F₅ — Constructive and digital

Digital (49, 89, 132)-net over F₅, using

1 times m-reduction [i] based on digital (49, 90, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 45, 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]

(49, 49+40, 138)-Net over F₅ — Digital

Digital (49, 89, 138)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+40, 2662)-Net in Base 5 — Upper bound on s

There is no (49, 89, 2663)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 162 021615 509289 869937 319333 412452 726895 101410 311171 363395 422385 > 5⁸⁹ [i]