MinT - Best Known (96−51, 96, s)-Nets in Base 7

Best Known (96−51, 96, s)-Nets in Base 7

(96−51, 96, 46)-Net over F₇ — Constructive and digital

Digital (45, 96, 46)-net over F₇, using

net from sequence [i] based on digital (45, 45)-sequence over F₇, using
- base reduction for sequences [i] based on digital (0, 45)-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]

(96−51, 96, 115)-Net over F₇ — Digital

Digital (45, 96, 115)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−51, 96, 2743)-Net in Base 7 — Upper bound on s

There is no (45, 96, 2744)-net in base 7, because

1 times m-reduction [i] would yield (45, 95, 2744)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 193 374128 294078 936854 754590 048717 257265 829366 997124 257776 923120 307890 686843 664081 > 7⁹⁵ [i]