MinT - Best Known (35−15, 35, s)-Nets in Base 7

Best Known (35−15, 35, s)-Nets in Base 7

(35−15, 35, 104)-Net over F₇ — Constructive and digital

Digital (20, 35, 104)-net over F₇, using

1 times m-reduction [i] based on digital (20, 36, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 18, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(35−15, 35, 156)-Net over F₇ — Digital

Digital (20, 35, 156)-net over F₇, using

1 times m-reduction [i] based on digital (20, 36, 156)-net over F₇, using
- trace code for nets [i] based on digital (2, 18, 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]

(35−15, 35, 7166)-Net in Base 7 — Upper bound on s

There is no (20, 35, 7167)-net in base 7, because

1 times m-reduction [i] would yield (20, 34, 7167)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 54169 717382 323661 979136 352215 > 7³⁴ [i]