MinT - Best Known (76−35, 76, s)-Nets in Base 7

Best Known (76−35, 76, s)-Nets in Base 7

(76−35, 76, 106)-Net over F₇ — Constructive and digital

Digital (41, 76, 106)-net over F₇, using

trace code for nets [i] based on digital (3, 38, 53)-net over F₄₉, using
- net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(76−35, 76, 184)-Net over F₇ — Digital

Digital (41, 76, 184)-net over F₇, using

trace code for nets [i] based on digital (3, 38, 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]

(76−35, 76, 6388)-Net in Base 7 — Upper bound on s

There is no (41, 76, 6389)-net in base 7, because

1 times m-reduction [i] would yield (41, 75, 6389)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2411 921149 829537 157892 419428 257969 888817 585846 223320 550347 816767 > 7⁷⁵ [i]