MinT - Best Known (23, 23+56, s)-Nets in Base 7

Best Known (23, 23+56, s)-Nets in Base 7

(23, 23+56, 30)-Net over F₇ — Constructive and digital

Digital (23, 79, 30)-net over F₇, using

net from sequence [i] based on digital (23, 29)-sequence over F₇, using
- Niederreiter sequence [i]

(23, 23+56, 72)-Net over F₇ — Digital

Digital (23, 79, 72)-net over F₇, using

t-expansion [i] based on digital (22, 79, 72)-net over F₇, using
- net from sequence [i] based on digital (22, 71)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 22 and N(F) ≥ 72, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(23, 23+56, 438)-Net in Base 7 — Upper bound on s

There is no (23, 79, 439)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 6 027081 898034 379000 966530 891834 158049 105706 952062 218738 996574 789337 > 7⁷⁹ [i]