MinT - Best Known (35−16, 35, s)-Nets in Base 7

Best Known (35−16, 35, s)-Nets in Base 7

(35−16, 35, 102)-Net over F₇ — Constructive and digital

Digital (19, 35, 102)-net over F₇, using

1 times m-reduction [i] based on digital (19, 36, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 18, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(35−16, 35, 128)-Net over F₇ — Digital

Digital (19, 35, 128)-net over F₇, using

1 times m-reduction [i] based on digital (19, 36, 128)-net over F₇, using
- trace code for nets [i] based on digital (1, 18, 64)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 63)-sequence over F₄₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 1 and N(F) ≥ 64, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

(35−16, 35, 3120)-Net in Base 7 — Upper bound on s

There is no (19, 35, 3121)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 379676 009842 967110 480288 128193 > 7³⁵ [i]