MinT - Best Known (80−42, 80, s)-Nets in Base 7

Best Known (80−42, 80, s)-Nets in Base 7

(80−42, 80, 39)-Net over F₇ — Constructive and digital

Digital (38, 80, 39)-net over F₇, using

net from sequence [i] based on digital (38, 38)-sequence over F₇, using
- base reduction for sequences [i] based on digital (0, 38)-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]

(80−42, 80, 105)-Net over F₇ — Digital

Digital (38, 80, 105)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−42, 80, 2384)-Net in Base 7 — Upper bound on s

There is no (38, 80, 2385)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 40 876429 239850 771655 337004 954265 086225 703638 191071 612531 083497 743623 > 7⁸⁰ [i]