MinT - Best Known (97−51, 97, s)-Nets in Base 7

Best Known (97−51, 97, s)-Nets in Base 7

(97−51, 97, 47)-Net over F₇ — Constructive and digital

Digital (46, 97, 47)-net over F₇, using

net from sequence [i] based on digital (46, 46)-sequence over F₇, using
- base reduction for sequences [i] based on digital (0, 46)-sequence over F₄₉, using
  - s-reduction 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]

(97−51, 97, 121)-Net over F₇ — Digital

Digital (46, 97, 121)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−51, 97, 2966)-Net in Base 7 — Upper bound on s

There is no (46, 97, 2967)-net in base 7, because

1 times m-reduction [i] would yield (46, 96, 2967)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1348 872418 952936 767376 047747 713479 346709 140003 253097 400472 342918 871044 556224 995835 > 7⁹⁶ [i]