MinT - Best Known (18, 34, s)-Nets in Base 7

Best Known (18, 34, s)-Nets in Base 7

(18, 34, 102)-Net over F₇ — Constructive and digital

Digital (18, 34, 102)-net over F₇, using

trace code for nets [i] based on digital (1, 17, 51)-net over F₄₉, using
- net from sequence [i] based on digital (1, 50)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(18, 34, 128)-Net over F₇ — Digital

Digital (18, 34, 128)-net over F₇, using

trace code for nets [i] based on digital (1, 17, 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]

(18, 34, 2445)-Net in Base 7 — Upper bound on s

There is no (18, 34, 2446)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 54224 435954 398206 810762 720913 > 7³⁴ [i]