MinT - Best Known (18−12, 18, s)-Nets in Base 49

Best Known (18−12, 18, s)-Nets in Base 49

(18−12, 18, 100)-Net over F₄₉ — Constructive and digital

Digital (6, 18, 100)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (0, 6, 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, 12, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

(18−12, 18, 7335)-Net in Base 49 — Upper bound on s

There is no (6, 18, 7336)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 2 653401 791757 859630 517013 997825 > 49¹⁸ [i]