MinT - Best Known (52−34, 52, s)-Nets in Base 49

Best Known (52−34, 52, s)-Nets in Base 49

(52−34, 52, 101)-Net over F₄₉ — Constructive and digital

Digital (18, 52, 101)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (0, 17, 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 (1, 35, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(52−34, 52, 122)-Net over F₄₉ — Digital

Digital (18, 52, 122)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(52−34, 52, 22108)-Net in Base 49 — Upper bound on s

There is no (18, 52, 22109)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 7771 345654 386850 575293 143028 163051 633468 313671 950334 563876 233974 512370 116974 647467 221105 > 49⁵² [i]