MinT - Best Known (47, 70, s)-Nets in Base 7

Best Known (47, 70, s)-Nets in Base 7

(47, 70, 202)-Net over F₇ — Constructive and digital

Digital (47, 70, 202)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (11, 22, 100)-net over F₇, using
  - trace code for nets [i] based on digital (0, 11, 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 (25, 48, 102)-net over F₇, using
  - trace code for nets [i] based on digital (1, 24, 51)-net over F₄₉, using
    - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
      - Niederreiter sequence [i]

(47, 70, 748)-Net over F₇ — Digital

Digital (47, 70, 748)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 70, 163649)-Net in Base 7 — Upper bound on s

There is no (47, 70, 163650)-net in base 7, because

1 times m-reduction [i] would yield (47, 69, 163650)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 20501 404412 765889 086263 459394 142244 564549 354089 352923 094201 > 7⁶⁹ [i]