MinT - Best Known (66−43, 66, s)-Nets in Base 7

Best Known (66−43, 66, s)-Nets in Base 7

(66−43, 66, 30)-Net over F₇ — Constructive and digital

Digital (23, 66, 30)-net over F₇, using

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

(66−43, 66, 72)-Net over F₇ — Digital

Digital (23, 66, 72)-net over F₇, using

t-expansion [i] based on digital (22, 66, 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]

(66−43, 66, 583)-Net in Base 7 — Upper bound on s

There is no (23, 66, 584)-net in base 7, because

1 times m-reduction [i] would yield (23, 65, 584)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 8 598665 463430 515447 505373 870616 673559 617253 984571 578545 > 7⁶⁵ [i]