MinT - Best Known (46−30, 46, s)-Nets in Base 49

Best Known (46−30, 46, s)-Nets in Base 49

(46−30, 46, 101)-Net over F₄₉ — Constructive and digital

Digital (16, 46, 101)-net over F₄₉, using

(u,Â u+v)-construction [i] based on
1. digital (0, 15, 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, 31, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(46−30, 46, 114)-Net over F₄₉ — Digital

Digital (16, 46, 114)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(46−30, 46, 20400)-Net in Base 49 — Upper bound on s

There is no (16, 46, 20401)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 561338 984558 892356 866674 041088 419796 572704 081882 128948 717547 175898 250259 049169 > 49⁴⁶ [i]