MinT - Best Known (10, 31, s)-Nets in Base 49

Best Known (10, 31, s)-Nets in Base 49

(10, 31, 100)-Net over F₄₉ — Constructive and digital

Digital (10, 31, 100)-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 (0, 21, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

(10, 31, 11095)-Net in Base 49 — Upper bound on s

There is no (10, 31, 11096)-net in base 49, because

1 times m-reduction [i] would yield (10, 30, 11096)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 508 342102 311987 813056 986969 210389 934610 873465 176321 > 49³⁰ [i]