MinT - Best Known (52−23, 52, s)-Nets in Base 7

Best Known (52−23, 52, s)-Nets in Base 7

(52−23, 52, 106)-Net over F₇ — Constructive and digital

Digital (29, 52, 106)-net over F₇, using

trace code for nets [i] based on digital (3, 26, 53)-net over F₄₉, using
- net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(52−23, 52, 184)-Net over F₇ — Digital

Digital (29, 52, 184)-net over F₇, using

trace code for nets [i] based on digital (3, 26, 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]

(52−23, 52, 6770)-Net in Base 7 — Upper bound on s

There is no (29, 52, 6771)-net in base 7, because

1 times m-reduction [i] would yield (29, 51, 6771)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 12 603934 674564 485975 658550 352884 790124 034687 > 7⁵¹ [i]