MinT - Best Known (92−69, 92, s)-Nets in Base 7

Best Known (92−69, 92, s)-Nets in Base 7

(92−69, 92, 30)-Net over F₇ — Constructive and digital

Digital (23, 92, 30)-net over F₇, using

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

(92−69, 92, 72)-Net over F₇ — Digital

Digital (23, 92, 72)-net over F₇, using

t-expansion [i] based on digital (22, 92, 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]

(92−69, 92, 390)-Net in Base 7 — Upper bound on s

There is no (23, 92, 391)-net in base 7, because

1 times m-reduction [i] would yield (23, 91, 391)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 83547 064034 936662 307066 867569 720400 154556 588948 823633 064205 554051 248744 781445 > 7⁹¹ [i]