MinT - Best Known (22−11, 22, s)-Nets in Base 7

Best Known (22−11, 22, s)-Nets in Base 7

(22−11, 22, 100)-Net over F₇ — Constructive and digital

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]

(22−11, 22, 1535)-Net in Base 7 — Upper bound on s

There is no (11, 22, 1536)-net in base 7, because

1 times m-reduction [i] would yield (11, 21, 1536)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 559152 451377 497089 > 7²¹ [i]