MinT - Best Known (26, 26+23, s)-Nets in Base 7

Best Known (26, 26+23, s)-Nets in Base 7

(26, 26+23, 102)-Net over F₇ — Constructive and digital

Digital (26, 49, 102)-net over F₇, using

1 times m-reduction [i] based on digital (26, 50, 102)-net over F₇, using
- trace code for nets [i] based on digital (1, 25, 51)-net over F₄₉, using
  - net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
    - Niederreiter sequence [i]

(26, 26+23, 128)-Net over F₇ — Digital

Digital (26, 49, 128)-net over F₇, using

1 times m-reduction [i] based on digital (26, 50, 128)-net over F₇, using
- trace code for nets [i] based on digital (1, 25, 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]

(26, 26+23, 3979)-Net in Base 7 — Upper bound on s

There is no (26, 49, 3980)-net in base 7, because

1 times m-reduction [i] would yield (26, 48, 3980)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 36763 107133 274820 376751 350529 625765 880609 > 7⁴⁸ [i]