MinT - Best Known (46, 46+53, s)-Nets in Base 7

Best Known (46, 46+53, s)-Nets in Base 7

(46, 46+53, 47)-Net over F₇ — Constructive and digital

Digital (46, 99, 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]

(46, 46+53, 115)-Net over F₇ — Digital

Digital (46, 99, 115)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+53, 2677)-Net in Base 7 — Upper bound on s

There is no (46, 99, 2678)-net in base 7, because

1 times m-reduction [i] would yield (46, 98, 2678)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 66069 581291 240757 013384 483841 246339 892142 507945 086556 967368 246854 810008 772127 076941 > 7⁹⁸ [i]