MinT - Best Known (30, 30+25, s)-Nets in Base 7

Best Known (30, 30+25, s)-Nets in Base 7

(30, 30+25, 104)-Net over F₇ — Constructive and digital

Digital (30, 55, 104)-net over F₇, using

1 times m-reduction [i] based on digital (30, 56, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 28, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(30, 30+25, 156)-Net over F₇ — Digital

Digital (30, 55, 156)-net over F₇, using

1 times m-reduction [i] based on digital (30, 56, 156)-net over F₇, using
- trace code for nets [i] based on digital (2, 28, 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]

(30, 30+25, 5592)-Net in Base 7 — Upper bound on s

There is no (30, 55, 5593)-net in base 7, because

1 times m-reduction [i] would yield (30, 54, 5593)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 4327 096082 111505 290846 665488 561006 766249 833697 > 7⁵⁴ [i]