MinT - Best Known (18, 18+14, s)-Nets in Base 7

Best Known (18, 18+14, s)-Nets in Base 7

(18, 18+14, 104)-Net over F₇ — Constructive and digital

Digital (18, 32, 104)-net over F₇, using

trace code for nets [i] based on digital (2, 16, 52)-net over F₄₉, using
- net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(18, 18+14, 156)-Net over F₇ — Digital

Digital (18, 32, 156)-net over F₇, using

trace code for nets [i] based on digital (2, 16, 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]

(18, 18+14, 4108)-Net in Base 7 — Upper bound on s

There is no (18, 32, 4109)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1106 270360 235078 866162 990167 > 7³² [i]