MinT - Best Known (62−28, 62, s)-Nets in Base 7

Best Known (62−28, 62, s)-Nets in Base 7

(62−28, 62, 106)-Net over F₇ — Constructive and digital

Digital (34, 62, 106)-net over F₇, using

trace code for nets [i] based on digital (3, 31, 53)-net over F₄₉, using
- net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(62−28, 62, 184)-Net over F₇ — Digital

Digital (34, 62, 184)-net over F₇, using

trace code for nets [i] based on digital (3, 31, 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]

(62−28, 62, 5561)-Net in Base 7 — Upper bound on s

There is no (34, 62, 5562)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 24922 202235 206363 693119 709671 939890 683057 770567 199149 > 7⁶² [i]