MinT - Best Known (33, 33+27, s)-Nets in Base 7

Best Known (33, 33+27, s)-Nets in Base 7

(33, 33+27, 106)-Net over F₇ — Constructive and digital

Digital (33, 60, 106)-net over F₇, using

trace code for nets [i] based on digital (3, 30, 53)-net over F₄₉, using
- net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(33, 33+27, 184)-Net over F₇ — Digital

Digital (33, 60, 184)-net over F₇, using

trace code for nets [i] based on digital (3, 30, 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]

(33, 33+27, 6458)-Net in Base 7 — Upper bound on s

There is no (33, 60, 6459)-net in base 7, because

1 times m-reduction [i] would yield (33, 59, 6459)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 72 604851 560749 978797 262409 508851 802937 404871 746139 > 7⁵⁹ [i]