MinT - Best Known (99−54, 99, s)-Nets in Base 7

Best Known (99−54, 99, s)-Nets in Base 7

(99−54, 99, 46)-Net over F₇ — Constructive and digital

Digital (45, 99, 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]

(99−54, 99, 107)-Net over F₇ — Digital

Digital (45, 99, 107)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−54, 99, 2267)-Net in Base 7 — Upper bound on s

There is no (45, 99, 2268)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 462778 837692 033205 062700 936433 020796 587065 404834 582246 490122 751860 453503 297892 987041 > 7⁹⁹ [i]