MinT - Best Known (71−33, 71, s)-Nets in Base 7

Best Known (71−33, 71, s)-Nets in Base 7

(71−33, 71, 104)-Net over F₇ — Constructive and digital

Digital (38, 71, 104)-net over F₇, using

1 times m-reduction [i] based on digital (38, 72, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 36, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(71−33, 71, 156)-Net over F₇ — Digital

Digital (38, 71, 156)-net over F₇, using

1 times m-reduction [i] based on digital (38, 72, 156)-net over F₇, using
- trace code for nets [i] based on digital (2, 36, 78)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 77)-sequence over F₄₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 2 and N(F) ≥ 78, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(71−33, 71, 5635)-Net in Base 7 — Upper bound on s

There is no (38, 71, 5636)-net in base 7, because

1 times m-reduction [i] would yield (38, 70, 5636)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 143830 872830 418387 714064 389113 911792 481743 069275 612362 759041 > 7⁷⁰ [i]