MinT - Best Known (76−54, 76, s)-Nets in Base 7

Best Known (76−54, 76, s)-Nets in Base 7

(76−54, 76, 29)-Net over F₇ — Constructive and digital

Digital (22, 76, 29)-net over F₇, using

t-expansion [i] based on digital (21, 76, 29)-net over F₇, using
- net from sequence [i] based on digital (21, 28)-sequence over F₇, using
  - Niederreiter sequence [i]

(76−54, 76, 72)-Net over F₇ — Digital

Digital (22, 76, 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]

(76−54, 76, 418)-Net in Base 7 — Upper bound on s

There is no (22, 76, 419)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 17648 480095 886976 699040 617559 968061 221561 318303 031869 403819 894687 > 7⁷⁶ [i]