MinT - Best Known (49−21, 49, s)-Nets in Base 7

Best Known (49−21, 49, s)-Nets in Base 7

(49−21, 49, 106)-Net over F₇ — Constructive and digital

Digital (28, 49, 106)-net over F₇, using

1 times m-reduction [i] based on digital (28, 50, 106)-net over F₇, using
- trace code for nets [i] based on digital (3, 25, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(49−21, 49, 184)-Net over F₇ — Digital

Digital (28, 49, 184)-net over F₇, using

1 times m-reduction [i] based on digital (28, 50, 184)-net over F₇, using
- trace code for nets [i] based on digital (3, 25, 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]

(49−21, 49, 8589)-Net in Base 7 — Upper bound on s

There is no (28, 49, 8590)-net in base 7, because

1 times m-reduction [i] would yield (28, 48, 8590)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 36711 065245 441405 028851 852443 405758 403133 > 7⁴⁸ [i]