MinT - Best Known (47−21, 47, s)-Nets in Base 7

Best Known (47−21, 47, s)-Nets in Base 7

(47−21, 47, 104)-Net over F₇ — Constructive and digital

Digital (26, 47, 104)-net over F₇, using

1 times m-reduction [i] based on digital (26, 48, 104)-net over F₇, using
- trace code for nets [i] based on digital (2, 24, 52)-net over F₄₉, using
  - net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(47−21, 47, 156)-Net over F₇ — Digital

Digital (26, 47, 156)-net over F₇, using

1 times m-reduction [i] based on digital (26, 48, 156)-net over F₇, using
- trace code for nets [i] based on digital (2, 24, 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]

(47−21, 47, 5818)-Net in Base 7 — Upper bound on s

There is no (26, 47, 5819)-net in base 7, because

1 times m-reduction [i] would yield (26, 46, 5819)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 749 603111 636753 750179 113690 603551 359549 > 7⁴⁶ [i]