MinT - Best Known (43−19, 43, s)-Nets in Base 7

Best Known (43−19, 43, s)-Nets in Base 7

(43−19, 43, 104)-Net over F₇ — Constructive and digital

Digital (24, 43, 104)-net over F₇, using

1 times m-reduction [i] based on digital (24, 44, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 22, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(43−19, 43, 156)-Net over F₇ — Digital

Digital (24, 43, 156)-net over F₇, using

1 times m-reduction [i] based on digital (24, 44, 156)-net over F₇, using
- trace code for nets [i] based on digital (2, 22, 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]

(43−19, 43, 6067)-Net in Base 7 — Upper bound on s

There is no (24, 43, 6068)-net in base 7, because

1 times m-reduction [i] would yield (24, 42, 6068)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 312283 075931 181253 186550 657992 670905 > 7⁴² [i]