MinT - Best Known (44, 44+48, s)-Nets in Base 7

Best Known (44, 44+48, s)-Nets in Base 7

(44, 44+48, 45)-Net over F₇ — Constructive and digital

Digital (44, 92, 45)-net over F₇, using

net from sequence [i] based on digital (44, 44)-sequence over F₇, using
- base reduction for sequences [i] based on digital (0, 44)-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]

(44, 44+48, 119)-Net over F₇ — Digital

Digital (44, 92, 119)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 44+48, 2820)-Net in Base 7 — Upper bound on s

There is no (44, 92, 2821)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 561837 760452 789773 605635 662838 534701 701527 059185 709308 037881 352252 848867 253761 > 7⁹² [i]