MinT - Best Known (57−25, 57, s)-Nets in Base 7

Best Known (57−25, 57, s)-Nets in Base 7

(57−25, 57, 106)-Net over F₇ — Constructive and digital

Digital (32, 57, 106)-net over F₇, using

1 times m-reduction [i] based on digital (32, 58, 106)-net over F₇, using
- trace code for nets [i] based on digital (3, 29, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(57−25, 57, 184)-Net over F₇ — Digital

Digital (32, 57, 184)-net over F₇, using

1 times m-reduction [i] based on digital (32, 58, 184)-net over F₇, using
- trace code for nets [i] based on digital (3, 29, 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]

(57−25, 57, 7737)-Net in Base 7 — Upper bound on s

There is no (32, 57, 7738)-net in base 7, because

1 times m-reduction [i] would yield (32, 56, 7738)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 211870 215375 988084 001765 210113 651476 108407 910169 > 7⁵⁶ [i]