MinT - Best Known (44−20, 44, s)-Nets in Base 7

Best Known (44−20, 44, s)-Nets in Base 7

(44−20, 44, 104)-Net over F₇ — Constructive and digital

Digital (24, 44, 104)-net over F₇, using

trace code for nets [i] based on digital (2, 22, 52)-net over F₄₉, using
- net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(44−20, 44, 156)-Net over F₇ — Digital

Digital (24, 44, 156)-net over F₇, using

trace code for nets [i] based on digital (2, 22, 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]

(44−20, 44, 3940)-Net in Base 7 — Upper bound on s

There is no (24, 44, 3941)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 15 296797 948369 672810 935466 070729 861209 > 7⁴⁴ [i]