MinT - Best Known (70−32, 70, s)-Nets in Base 7

Best Known (70−32, 70, s)-Nets in Base 7

(70−32, 70, 106)-Net over F₇ — Constructive and digital

Digital (38, 70, 106)-net over F₇, using

trace code for nets [i] based on digital (3, 35, 53)-net over F₄₉, using
- net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(70−32, 70, 184)-Net over F₇ — Digital

Digital (38, 70, 184)-net over F₇, using

trace code for nets [i] based on digital (3, 35, 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]

(70−32, 70, 5635)-Net in Base 7 — Upper bound on s

There is no (38, 70, 5636)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 143830 872830 418387 714064 389113 911792 481743 069275 612362 759041 > 7⁷⁰ [i]