MinT - Best Known (34−14, 34, s)-Nets in Base 7

Best Known (34−14, 34, s)-Nets in Base 7

(34−14, 34, 106)-Net over F₇ — Constructive and digital

Digital (20, 34, 106)-net over F₇, using

trace code for nets [i] based on digital (3, 17, 53)-net over F₄₉, using
- net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(34−14, 34, 184)-Net over F₇ — Digital

Digital (20, 34, 184)-net over F₇, using

trace code for nets [i] based on digital (3, 17, 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]

(34−14, 34, 7166)-Net in Base 7 — Upper bound on s

There is no (20, 34, 7167)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 54169 717382 323661 979136 352215 > 7³⁴ [i]