MinT - Best Known (33−14, 33, s)-Nets in Base 7

Best Known (33−14, 33, s)-Nets in Base 7

(33−14, 33, 104)-Net over F₇ — Constructive and digital

Digital (19, 33, 104)-net over F₇, using

1 times m-reduction [i] based on digital (19, 34, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 17, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(33−14, 33, 156)-Net over F₇ — Digital

Digital (19, 33, 156)-net over F₇, using

1 times m-reduction [i] based on digital (19, 34, 156)-net over F₇, using
- trace code for nets [i] based on digital (2, 17, 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]

(33−14, 33, 5425)-Net in Base 7 — Upper bound on s

There is no (19, 33, 5426)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7732 496027 781409 547324 442433 > 7³³ [i]