MinT - Best Known (31, 31+20, s)-Nets in Base 49

Best Known (31, 31+20, s)-Nets in Base 49

(31, 31+20, 394)-Net over F₄₉ — Constructive and digital

Digital (31, 51, 394)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (0, 10, 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 (21, 41, 344)-net over F₄₉, using
  - net from sequence [i] based on digital (21, 343)-sequence over F₄₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 21 and N(F) ≥ 344, using
      - the Hermitian function field over F₄₉ [i]

(31, 31+20, 5696)-Net over F₄₉ — Digital

Digital (31, 51, 5696)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(31, 31+20, large)-Net in Base 49 — Upper bound on s

There is no (31, 51, large)-net in base 49, because

18 times m-reduction [i] would yield (31, 33, large)-net in base 49, but
- mutually orthogonal hypercube bound [i]