MinT - Best Known (55−24, 55, s)-Nets in Base 7

Best Known (55−24, 55, s)-Nets in Base 7

(55−24, 55, 106)-Net over F₇ — Constructive and digital

Digital (31, 55, 106)-net over F₇, using

1 times m-reduction [i] based on digital (31, 56, 106)-net over F₇, using
- trace code for nets [i] based on digital (3, 28, 53)-net over F₄₉, using
  - net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(55−24, 55, 184)-Net over F₇ — Digital

Digital (31, 55, 184)-net over F₇, using

1 times m-reduction [i] based on digital (31, 56, 184)-net over F₇, using
- trace code for nets [i] based on digital (3, 28, 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]

(55−24, 55, 6577)-Net in Base 7 — Upper bound on s

There is no (31, 55, 6578)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 30237 148475 303702 943559 443182 368702 750317 712537 > 7⁵⁵ [i]