MinT - Best Known (41−17, 41, s)-Nets in Base 7

Best Known (41−17, 41, s)-Nets in Base 7

(41−17, 41, 106)-Net over F₇ — Constructive and digital

Digital (24, 41, 106)-net over F₇, using

1 times m-reduction [i] based on digital (24, 42, 106)-net over F₇, using
- trace code for nets [i] based on digital (3, 21, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(41−17, 41, 184)-Net over F₇ — Digital

Digital (24, 41, 184)-net over F₇, using

1 times m-reduction [i] based on digital (24, 42, 184)-net over F₇, using
- trace code for nets [i] based on digital (3, 21, 92)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 91)-sequence over F₄₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 3 and N(F) ≥ 92, using
      - a curve from the manYPoints database [i]

(41−17, 41, 10539)-Net in Base 7 — Upper bound on s

There is no (24, 41, 10540)-net in base 7, because

1 times m-reduction [i] would yield (24, 40, 10540)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 6368 057651 899291 036276 529785 846849 > 7⁴⁰ [i]