MinT - Best Known (38−17, 38, s)-Nets in Base 7

Best Known (38−17, 38, s)-Nets in Base 7

(38−17, 38, 104)-Net over F₇ — Constructive and digital

Digital (21, 38, 104)-net over F₇, using

trace code for nets [i] based on digital (2, 19, 52)-net over F₄₉, using
- net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(38−17, 38, 156)-Net over F₇ — Digital

Digital (21, 38, 156)-net over F₇, using

trace code for nets [i] based on digital (2, 19, 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]

(38−17, 38, 5078)-Net in Base 7 — Upper bound on s

There is no (21, 38, 5079)-net in base 7, because

1 times m-reduction [i] would yield (21, 37, 5079)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 18 587407 919253 156033 081301 722961 > 7³⁷ [i]