MinT - Best Known (27, 43, s)-Nets in Base 49

Best Known (27, 43, s)-Nets in Base 49

(27, 43, 450)-Net over F₄₉ — Constructive and digital

Digital (27, 43, 450)-net over F₄₉, using

1 times m-reduction [i] based on digital (27, 44, 450)-net over F₄₉, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 1, 50)-net over F₄₉, using
    - s-reduction based on digital (0, 1, s)-net over F₄₉ with arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  2. digital (0, 2, 50)-net over F₄₉, using
    - kÂ =Â 2 construction [i]
  3. digital (0, 2, 50)-net over F₄₉ (see above)
  4. digital (0, 2, 50)-net over F₄₉ (see above)
  5. digital (0, 3, 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]
  6. digital (0, 4, 50)-net over F₄₉, using
    - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)
  7. digital (0, 5, 50)-net over F₄₉, using
    - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)
  8. digital (0, 8, 50)-net over F₄₉, using
    - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)
  9. digital (0, 17, 50)-net over F₄₉, using
    - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

(27, 43, 9378)-Net over F₄₉ — Digital

Digital (27, 43, 9378)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(27, 43, large)-Net in Base 49 — Upper bound on s

There is no (27, 43, large)-net in base 49, because

14 times m-reduction [i] would yield (27, 29, large)-net in base 49, but
- mutually orthogonal hypercube bound [i]