MinT - Best Known (34−23, 34, s)-Nets in Base 49

Best Known (34−23, 34, s)-Nets in Base 49

(34−23, 34, 100)-Net over F₄₉ — Constructive and digital

Digital (11, 34, 100)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (0, 11, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
      - the rational function field F₄₉(x) [i]
    - Niederreiter sequence [i]
2. digital (0, 23, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

(34−23, 34, 12027)-Net in Base 49 — Upper bound on s

There is no (11, 34, 12028)-net in base 49, because

1 times m-reduction [i] would yield (11, 33, 12028)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 59 800078 515419 850191 801021 114486 307176 327872 265640 821185 > 49³³ [i]