MinT - Best Known (99−41, 99, s)-Nets in Base 5

Best Known (99−41, 99, s)-Nets in Base 5

(99−41, 99, 132)-Net over F₅ — Constructive and digital

Digital (58, 99, 132)-net over F₅, using

9 times m-reduction [i] based on digital (58, 108, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 54, 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]

(99−41, 99, 200)-Net over F₅ — Digital

Digital (58, 99, 200)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−41, 99, 5508)-Net in Base 5 — Upper bound on s

There is no (58, 99, 5509)-net in base 5, because

1 times m-reduction [i] would yield (58, 98, 5509)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 315 748115 250353 351369 641727 286802 625191 576510 858691 767221 222648 629425 > 5⁹⁸ [i]