MinT - Best Known (47, 47+58, s)-Nets in Base 7

Best Known (47, 47+58, s)-Nets in Base 7

(47, 47+58, 48)-Net over F₇ — Constructive and digital

Digital (47, 105, 48)-net over F₇, using

net from sequence [i] based on digital (47, 47)-sequence over F₇, using
- base reduction for sequences [i] based on digital (0, 47)-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]

(47, 47+58, 107)-Net over F₇ — Digital

Digital (47, 105, 107)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+58, 2213)-Net in Base 7 — Upper bound on s

There is no (47, 105, 2214)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 54499 629502 967495 398724 331955 492447 364520 582863 646026 822736 544104 777983 818214 915313 699565 > 7¹⁰⁵ [i]