MinT - Best Known (72−34, 72, s)-Nets in Base 7

Best Known (72−34, 72, s)-Nets in Base 7

(72−34, 72, 104)-Net over F₇ — Constructive and digital

Digital (38, 72, 104)-net over F₇, using

trace code for nets [i] based on digital (2, 36, 52)-net over F₄₉, using
- net from sequence [i] based on digital (2, 51)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(72−34, 72, 156)-Net over F₇ — Digital

Digital (38, 72, 156)-net over F₇, using

trace code for nets [i] based on digital (2, 36, 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]

(72−34, 72, 4528)-Net in Base 7 — Upper bound on s

There is no (38, 72, 4529)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 7 033434 407309 202000 228695 631368 301866 530842 805352 005026 782887 > 7⁷² [i]