MinT - Best Known (12, 12+11, s)-Nets in Base 7

Best Known (12, 12+11, s)-Nets in Base 7

(12, 12+11, 100)-Net over F₇ — Constructive and digital

Digital (12, 23, 100)-net over F₇, using

1 times m-reduction [i] based on digital (12, 24, 100)-net over F₇, using
- trace code for nets [i] based on digital (0, 12, 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]

(12, 12+11, 2267)-Net in Base 7 — Upper bound on s

There is no (12, 23, 2268)-net in base 7, because

1 times m-reduction [i] would yield (12, 22, 2268)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3 912911 895411 626185 > 7²² [i]